After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
Then she reacted suddenly, with an expression of surprise on her face.
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
[Golden reward mission starts!]
"... According to Euler's formula, by transforming Equation 2, we can get that for any integer n>1, there is ζ(2n)=b(n)π^(2n)."
"Very standard proof method."
"Can't answer? ζ(3) seems simpler than ζ(2n), right? The latter also has an unknown number in the parentheses."
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
During this time, he could do something else first.
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
The familiar warm current gradually climbed up his spine and into his brain. As the feeling of being soaked in a hot spring spread along the nerve network to his limbs, Lu Zhou felt that his spirit was higher than ever and his thoughts were clearer than ever.
When he met the only person in the office, he saw that the little girl's face gradually turned red and she stammered.
"good."
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
Since they are called legends, they must be more advanced than golden mission cards.
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
[Task reward: 10,000 points, 2 million mathematical experience, and a "Legend" task card.]
Such a simple question…
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
"show me."
[Golden reward mission starts!]
It feels like...
"Page 3, line 16."
"Page 3, line 16."
[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]
What the hell is this thing? !
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
But so what
[Task reward: 10,000 points, 2 million mathematical experience, and a "Legend" task card.]
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
[Requirement: Solve the Riemann Hypothesis within three years!]
Han Mengqi answered honestly: "... I guessed it."
Looking at Han Mengqi who was waiting for him, Lu Zhou put down the coffee cup in his hand and continued to ask.
Taking a deep breath, she paused for a moment before continuing.
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
[Task reward: 10,000 points, 2 million mathematical experience, and a "Legend" task card.]
"Thanks."
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
Hey hey
"...can we solve the Riemann Hypothesis within three years?"
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
After hearing Lu Zhou's words, Han Mengqi was slightly stunned for a moment.
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
ζ(3)…
"Although this is the top crown in mathematics, in three years..."
"You may be looking down on me too much."
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
"The 'Legend' mission card is really exciting..."
"You may be looking down on me too much."
"...I'm very smart."
Han Mengqi raised her chin proudly.
Han Mengqi raised her chin proudly.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
[Golden reward mission starts!]
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
"You're welcome... Well, I've already finished the questions you assigned me."
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
"There is an answer." Looking at Han Mengqi, Lu Zhou smiled and said in a serious tone, "There is an answer to any mathematical problem, but we don't know it yet. And when you go from a master's degree to a Ph.D. Later, the challenge is also here, you have to learn to find a way to the exit of the maze on your own, come up with the idea, and then realize it.”
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
The line at the top of the article was the question he assigned her last month.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
Han Mengqi answered honestly: "... I guessed it."
Han Mengqi raised her chin proudly.
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
But so what
The line at the top of the article was the question he assigned her last month.
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
There has never been a problem that bothered him for three years...
"...I saw that you were sleeping soundly, so I put it on for you."
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
Lu Zhou had no doubt that he could solve this problem within three years.
"show me."
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
"At that time, you will be able to graduate from me."
"What... are you bringing this kind of unanswered question... to bully me?"
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
This is not only a kind of mathematical intuition, but also the confidence brought by his long-term success in the field of mathematics!
[Requirement: Solve the Riemann Hypothesis within three years!]
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
"Also...transcendental numbers?"
"You ask!"
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
"The 'Legend' mission card is really exciting..."
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
"There is an answer." Looking at Han Mengqi, Lu Zhou smiled and said in a serious tone, "There is an answer to any mathematical problem, but we don't know it yet. And when you go from a master's degree to a Ph.D. Later, the challenge is also here, you have to learn to find a way to the exit of the maze on your own, come up with the idea, and then realize it.”
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
"You're welcome... Well, I've already finished the questions you assigned me."
Since they are called legends, they must be more advanced than golden mission cards.
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
There has never been a problem that bothered him for three years...
"...can we solve the Riemann Hypothesis within three years?"
"Very standard proof method."
"...I saw that you were sleeping soundly, so I put it on for you."
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
"After you successfully answered the first question, I have already made up my mind."
It feels like...
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
…
"show me."
What the hell is this thing? !
"Thanks."
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
Such a simple question…
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
Since they are called legends, they must be more advanced than golden mission cards.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
This is not only a kind of mathematical intuition, but also the confidence brought by his long-term success in the field of mathematics!
However, just when she was about to answer this question, she was stunned.
The familiar warm current gradually climbed up his spine and into his brain. As the feeling of being soaked in a hot spring spread along the nerve network to his limbs, Lu Zhou felt that his spirit was higher than ever and his thoughts were clearer than ever.
During this time, he could do something else first.
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"I will personally confirm this."
One step closer to the omniscient and omnipotent God.
It feels like...
Taking a deep breath, she paused for a moment before continuing.
Lu Zhou smiled lightly.
Lu Zhou had no doubt that he could solve this problem within three years.
Looking at the confused Han Mengqi, Lu Zhou smiled and asked.
One step closer to the omniscient and omnipotent God.
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
"Although this is the top crown in mathematics, in three years..."
"Very standard proof method."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
"If you can take a step forward in this direction, even a small step, as long as it is a result that is recognized by the academic community."
However, just when she was about to answer this question, she was stunned.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
"The 'Legend' mission card is really exciting..."
"You ask!"
"Although this is the top crown in mathematics, in three years..."
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
One step closer to the omniscient and omnipotent God.
Taking a deep breath, she paused for a moment before continuing.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
"I will personally confirm this."
Looking at Han Mengqi who was waiting for him, Lu Zhou put down the coffee cup in his hand and continued to ask.
When he met the only person in the office, he saw that the little girl's face gradually turned red and she stammered.
"What... are you bringing this kind of unanswered question... to bully me?"
"good."
"...I saw that you were sleeping soundly, so I put it on for you."
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
The familiar warm current gradually climbed up his spine and into his brain. As the feeling of being soaked in a hot spring spread along the nerve network to his limbs, Lu Zhou felt that his spirit was higher than ever and his thoughts were clearer than ever.
"As for the second question, it is your research topic."
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
"Although this is the top crown in mathematics, in three years..."
Looking at Han Mengqi who was explaining hurriedly, Lu Zhou smiled and said.
[Task reward: 10,000 points, 2 million mathematical experience, and a "Legend" task card.]
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
[Requirement: Solve the Riemann Hypothesis within three years!]
Han Mengqi raised her chin proudly.
This is not only a kind of mathematical intuition, but also the confidence brought by his long-term success in the field of mathematics!
"Thanks."
"Thanks."
"What... are you bringing this kind of unanswered question... to bully me?"
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
Since they are called legends, they must be more advanced than golden mission cards.
"good."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
"You're welcome... Well, I've already finished the questions you assigned me."
"The 'Legend' mission card is really exciting..."
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
The familiar warm current gradually climbed up his spine and into his brain. As the feeling of being soaked in a hot spring spread along the nerve network to his limbs, Lu Zhou felt that his spirit was higher than ever and his thoughts were clearer than ever.
"At that time, you will be able to graduate from me."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
Han Mengqi answered honestly: "... I guessed it."
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
Such a simple question…
"I don't know if it's right, but... I thought about it myself."
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
The familiar warm current gradually climbed up his spine and into his brain. As the feeling of being soaked in a hot spring spread along the nerve network to his limbs, Lu Zhou felt that his spirit was higher than ever and his thoughts were clearer than ever.
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
"As for the second question, it is your research topic."
"show me."
After hearing Lu Zhou's words, Han Mengqi was slightly stunned for a moment.
Looking down, Lu Zhou spent about five minutes reading the calculation process, which lasted five or six pages, from beginning to end, and then gave a more pertinent evaluation.
"Can't answer? ζ(3) seems simpler than ζ(2n), right? The latter also has an unknown number in the parentheses."
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
Lu Zhou smiled lightly.
Lu Zhou smiled and asked, "Oh? Why?"
There has never been a problem that bothered him for three years...
"As for the second question, it is your research topic."
"At that time, you will be able to graduate from me."
ζ(3)!
The line at the top of the article was the question he assigned her last month.
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
Lu Zhou smiled lightly.
Hey hey
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
[For any real number s>1, define ζ(s)=Σ1/(m^s), and verify that ζ(2n) is a transcendental number.]
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
After a while, he asked in a tentative tone.
Looking down, Lu Zhou spent about five minutes reading the calculation process, which lasted five or six pages, from beginning to end, and then gave a more pertinent evaluation.
Hearing this question, Han Mengqi secretly breathed a sigh of relief.
ζ(3)!
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
"Very standard proof method."
Since they are called legends, they must be more advanced than golden mission cards.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
After hearing Lu Zhou's words, Han Mengqi was slightly stunned for a moment.
Han Mengqi answered honestly: "... I guessed it."
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
[Requirement: Solve the Riemann Hypothesis within three years!]
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
Looking at the confused Han Mengqi, Lu Zhou smiled and asked.
However, just when she was about to answer this question, she was stunned.
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
[Golden reward mission starts!]
[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
[For any real number s>1, define ζ(s)=Σ1/(m^s), and verify that ζ(2n) is a transcendental number.]
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
There has never been a problem that bothered him for three years...
ζ(3)!
"I don't know if it's right, but... I thought about it myself."
Since they are called legends, they must be more advanced than golden mission cards.
"...I'm very smart."
"good."
"I don't know if it's right, but... I thought about it myself."
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
ζ(3)!
Her forehead was so hot that steam was almost coming out. Han Mengqi was at a loss and looked away from Lu Zhou. She walked forward with small steps and handed out the almost full stack of A4 paper in her hand with an anxious look on her face.
"You may be looking down on me too much."
Looking at Han Mengqi who was waiting for him, Lu Zhou put down the coffee cup in his hand and continued to ask.
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
Lu Zhou smiled lightly.
"I don't know if it's right, but... I thought about it myself."
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
"I will personally confirm this."
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
Han Mengqi raised her chin proudly.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
When he met the only person in the office, he saw that the little girl's face gradually turned red and she stammered.
Looking at Han Mengqi who was explaining hurriedly, Lu Zhou smiled and said.
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
"What... are you bringing this kind of unanswered question... to bully me?"
"You ask!"
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
[Requirement: Solve the Riemann Hypothesis within three years!]
"At that time, you will be able to graduate from me."
"At that time, you will be able to graduate from me."
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
"Page 3, line 16."
Since they are called legends, they must be more advanced than golden mission cards.
[Task reward: 10,000 points, 2 million mathematical experience, and a "Legend" task card.]
"...I saw that you were sleeping soundly, so I put it on for you."
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
Lu Zhou smiled and nodded.
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
The line at the top of the article was the question he assigned her last month.
The sound of paper turning was heard, and Han Mengqi quickly found the location of the row.
Lu Zhou smiled and asked, "Oh? Why?"
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
After a while, he asked in a tentative tone.
"If you can take a step forward in this direction, even a small step, as long as it is a result that is recognized by the academic community."
ζ(3)…
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
When he met the only person in the office, he saw that the little girl's face gradually turned red and she stammered.
Picking up the slightly cold coffee cup on the table and taking a sip, Lu Zhou paused for a moment and continued: "Explain in detail how to derive ζ(2n) from Equation 2 as a transcendental number."
"The 'Legend' mission card is really exciting..."
During this time, he could do something else first.
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"If you can take a step forward in this direction, even a small step, as long as it is a result that is recognized by the academic community."
Taking a deep breath, she paused for a moment before continuing.
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
"After you successfully answered the first question, I have already made up my mind."
The sound of paper turning was heard, and Han Mengqi quickly found the location of the row.
Hearing this question, Han Mengqi secretly breathed a sigh of relief.
Hearing this question, Han Mengqi secretly breathed a sigh of relief.
What the hell is this thing? !
"It's not surprising that you don't know, because Euler, who wrote Euler's formula, didn't know it either. It wasn't until 1978 that the French mathematician R. Ap'ery proved that ζ(3) is not a rational number, and about ζ(5) It’s not a rational number, we don’t know it yet.”
[For any real number s>1, define ζ(s)=Σ1/(m^s), and verify that ζ(2n) is a transcendental number.]
It feels like...
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
"... According to Euler's formula, by transforming Equation 2, we can get that for any integer n>1, there is ζ(2n)=b(n)π^(2n)."
Lu Zhou smiled lightly.
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
"You're welcome... Well, I've already finished the questions you assigned me."
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
The line at the top of the article was the question he assigned her last month.
"Page 3, line 16."
Taking a deep breath, she paused for a moment before continuing.
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
Hearing this question, Han Mengqi secretly breathed a sigh of relief.
"... According to Euler's formula, by transforming Equation 2, we can get that for any integer n>1, there is ζ(2n)=b(n)π^(2n)."
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
"Very standard proof method."
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"... According to Euler's formula, by transforming Equation 2, we can get that for any integer n>1, there is ζ(2n)=b(n)π^(2n)."
"good."
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
However, just when she was about to answer this question, she was stunned.
"Also...transcendental numbers?"
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
"Very standard proof method."
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
"Page 3, line 16."
"Also...transcendental numbers?"
Then she reacted suddenly, with an expression of surprise on her face.
ζ(3)…
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
"I don't know if it's right, but... I thought about it myself."
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
The sound of paper turning was heard, and Han Mengqi quickly found the location of the row.
"The 'Legend' mission card is really exciting..."
ζ(3)!
Han Mengqi raised her chin proudly.
"good."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
Lu Zhou smiled and asked, "Oh? Why?"
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
ζ(3)!
"But don't be too proud. This question is just to test whether you completed the paper yourself. The next question is the real challenge."
"What... are you bringing this kind of unanswered question... to bully me?"
"At that time, you will be able to graduate from me."
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
"You may be looking down on me too much."
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
"Also...transcendental numbers?"
Looking at Han Mengqi who was waiting for him, Lu Zhou put down the coffee cup in his hand and continued to ask.
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
Han Mengqi answered honestly: "... I guessed it."
"What... are you bringing this kind of unanswered question... to bully me?"
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Looking at the confused Han Mengqi, Lu Zhou smiled and asked.
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
"... According to Euler's formula, by transforming Equation 2, we can get that for any integer n>1, there is ζ(2n)=b(n)π^(2n)."
[Golden reward mission starts!]
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
Such a simple question…
The sound of paper turning was heard, and Han Mengqi quickly found the location of the row.
The line at the top of the article was the question he assigned her last month.
Han Mengqi raised her chin proudly.
There has never been a problem that bothered him for three years...
[Requirement: Solve the Riemann Hypothesis within three years!]
"You're welcome... Well, I've already finished the questions you assigned me."
However, just when she was about to answer this question, she was stunned.
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
"good."
"At that time, you will be able to graduate from me."
[Requirement: Solve the Riemann Hypothesis within three years!]
"Now that you have proved that ζ(2n) is a transcendental number, what I want to ask is, what about ζ(3)?"
ζ(3)!
Hey hey
"Also...transcendental numbers?"
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
ζ(3)…
During this time, he could do something else first.
Lu Zhou had no doubt that he could solve this problem within three years.
There has never been a problem that bothered him for three years...
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
But so what
During this time, he could do something else first.
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
Hey hey
"The 'Legend' mission card is really exciting..."
The line at the top of the article was the question he assigned her last month.
"Thanks."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
Hearing this question, Han Mengqi secretly breathed a sigh of relief.
After hearing Lu Zhou's words, Han Mengqi was slightly stunned for a moment.
What the hell is this thing? !
It is not easy to prove the Riemann Hypothesis. Even if the quasi-Riemann Hypothesis is proved, it only opens a path to the top of the mountain. It will take a lot of effort to reach the top of the mountain.
Looking at Han Mengqi who was waiting for him, Lu Zhou put down the coffee cup in his hand and continued to ask.
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
"show me."
Lu Zhou smiled and nodded.
Looking at the confused Han Mengqi, Lu Zhou smiled and asked.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
"Can't answer? ζ(3) seems simpler than ζ(2n), right? The latter also has an unknown number in the parentheses."
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
"But don't be too proud. This question is just to test whether you completed the paper yourself. The next question is the real challenge."
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
"It's surprising. I thought you would spend more time proving it, but I didn't expect you to finish it this year."
ζ(3)…
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
[Requirement: Solve the Riemann Hypothesis within three years!]
"The transcendence of the Riemann zeta function at odd positive integer points has always been a classic issue in the field of analytical number theory. According to Euler's formula and the properties of Bernoulli numbers, it can be easily proved that ζ (2n) is a transcendental number, Therefore, people conjecture that for any integer n>1, ζ(2n+1) is also a transcendental number."
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
"It's not surprising that you don't know, because Euler, who wrote Euler's formula, didn't know it either. It wasn't until 1978 that the French mathematician R. Ap'ery proved that ζ(3) is not a rational number, and about ζ(5) It’s not a rational number, we don’t know it yet.”
After a while, he asked in a tentative tone.
Lu Zhou moved his shoulders slightly and felt the weight on his shoulders. He reached out and touched it and found that his shoulders were covered with a blanket.
[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]
"Also...transcendental numbers?"
[Explanation: The throne of the old era has stood for a century and a half. The beginning of the new era will surely be preceded by the end of the old era! The first step on the road to the future starts with mathematics...]
"show me."
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
Lu Zhou smiled and asked, "Oh? Why?"
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
Han Mengqi answered honestly: "... I guessed it."
[Requirement: Solve the Riemann Hypothesis within three years!]
"You ask!"
Taking a deep breath, she paused for a moment before continuing.
"What... are you bringing this kind of unanswered question... to bully me?"
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
Han Mengqi answered honestly: "... I guessed it."
"...can we solve the Riemann Hypothesis within three years?"
Lu Zhou had no doubt that he could solve this problem within three years.
"What... are you bringing this kind of unanswered question... to bully me?"
"It's not surprising that you don't know, because Euler, who wrote Euler's formula, didn't know it either. It wasn't until 1978 that the French mathematician R. Ap'ery proved that ζ(3) is not a rational number, and about ζ(5) It’s not a rational number, we don’t know it yet.”
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
"Although this is the top crown in mathematics, in three years..."
"There is an answer." Looking at Han Mengqi, Lu Zhou smiled and said in a serious tone, "There is an answer to any mathematical problem, but we don't know it yet. And when you go from a master's degree to a Ph.D. Later, the challenge is also here, you have to learn to find a way to the exit of the maze on your own, come up with the idea, and then realize it.”
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
"...I'm very smart."
Looking down, Lu Zhou spent about five minutes reading the calculation process, which lasted five or six pages, from beginning to end, and then gave a more pertinent evaluation.
Upon hearing that there was no answer to the question Lu Zhou asked him, Han Mengqi suddenly said angrily.
"Thanks."
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
"What... are you bringing this kind of unanswered question... to bully me?"
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
"There is an answer." Looking at Han Mengqi, Lu Zhou smiled and said in a serious tone, "There is an answer to any mathematical problem, but we don't know it yet. And when you go from a master's degree to a Ph.D. Later, the challenge is also here, you have to learn to find a way to the exit of the maze on your own, come up with the idea, and then realize it.”
Although he didn't know what was hidden on the back of the card, Lu Zhou felt a surge of emotion in his heart when he thought of the word legend that defined it...
Without further ado, Lu Zhou took the stack of A4 paper from the little girl's hand and glanced at it roughly.
After hearing Lu Zhou's words, Han Mengqi was slightly stunned for a moment.
"good."
Looking away from the proof process in his hands, Lu Zhou glanced at the calendar, and then handed the proof process back to Han Mengqi, who was waiting for the results with an anxious look.
There has never been a problem that bothered him for three years...
"I don't know if it's right, but... I thought about it myself."
"Thanks."
Lu Zhou looked at the content on the holographic panel from beginning to end without expression, and said to himself thoughtfully.
"Thanks."
One step closer to the omniscient and omnipotent God.
Then she reacted suddenly, with an expression of surprise on her face.
However, just when she was about to answer this question, she was stunned.
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
The line at the top of the article was the question he assigned her last month.
It didn't take long to transform the brain, and the warm current that climbed up the spine disappeared completely in an instant.
"The transcendence of the Riemann zeta function at odd positive integer points has always been a classic issue in the field of analytical number theory. According to Euler's formula and the properties of Bernoulli numbers, it can be easily proved that ζ (2n) is a transcendental number, Therefore, people conjecture that for any integer n>1, ζ(2n+1) is also a transcendental number."
The line at the top of the article was the question he assigned her last month.
Hearing this compliment, the corners of her pressed lips couldn't help but curl up with a hint of pride, and Han Mengqi snorted softly.
"Wait, wait a minute, you mean you decided to accept me as your disciple?!"
Although the plan for the mass projector is on the work agenda of the Lunar Orbit Construction Committee, we don’t know how long it will take to build it.
"What... are you bringing this kind of unanswered question... to bully me?"
Lu Zhou smiled and nodded.
Looking at Lu Zhou who was about to ask a question, Han Mengqi braced herself up and spoke in a prepared manner.
It feels like...
Anyway, all projects on the moon rely on idle time. The tasks will not run if they are placed there. At most, they will just be delayed for a while to complete.
Lu Zhou had no doubt that he could solve this problem within three years.
Such a simple question…
"After you successfully answered the first question, I have already made up my mind."
After listening to Han Mengqi's explanation, Lu Zhou nodded approvingly.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
"As for the second question, it is your research topic."
The line at the top of the article was the question he assigned her last month.
Lu Zhou smiled and asked, "Oh? Why?"
Seeing the little girl lowering her head honestly, Lu Zhou smiled, paused for a moment and continued.
After leaving the system space, Lu Zhou, who was sitting in the office, slowly opened his eyes and came back to his senses from closing his eyes to rest.
With that said, Lu Zhou stood up from behind his desk, walked to the blackboard in the office, picked up a half-used piece of chalk, and wrote on the blackboard while talking.
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
"Where b(2n) is a sequence of rational numbers, that is, the Bernoulli number. It is obvious that ζ(2) is π^2 multiplied by a special rational number, and ζ(4) is π^4 multiplied by a special rational number... Therefore, we completely It is clear that ζ(2), ζ(4)... are all rational numbers. And because π is a transcendental number, of course these function values are also transcendental numbers."
After looking at the unfolded task bar and thinking about it for about five minutes, Lu Zhou finally chose to use the reward task card.
"The transcendence of the Riemann zeta function at odd positive integer points has always been a classic issue in the field of analytical number theory. According to Euler's formula and the properties of Bernoulli numbers, it can be easily proved that ζ (2n) is a transcendental number, Therefore, people conjecture that for any integer n>1, ζ(2n+1) is also a transcendental number."
Before she came, she was already prepared to be made difficult by Lu Zhou. Unexpectedly, Lu Zhou did not make things difficult for her with that kind of particularly difficult question, but just asked a very basic one.
After confirming the mission description and requirements for the last time, Lu Zhou smiled faintly, lightly moved his index finger across the holographic screen, and closed the updated taskbar.
[Requirement: Solve the Riemann Hypothesis within three years!]
Lu Zhou smiled lightly.
"I will personally confirm this."
"...can we solve the Riemann Hypothesis within three years?"
"The best result so far is that there are countless ζ(2n+1) that are irrational numbers. However, in mathematics, the difference between infinity and infinity is only as far away as infinity."
Lu Zhou smiled and asked, "Oh? Why?"
Such a simple question…
"Well..." Han Mengqi's cheeks bulged, biting her lower lip and thinking hard, but she couldn't say a word.
"Also...transcendental numbers?"
Lu Zhou smiled lightly.
"If you can take a step forward in this direction, even a small step, as long as it is a result that is recognized by the academic community."
"I don't know if it's right, but... I thought about it myself."
"After you successfully answered the first question, I have already made up my mind."
The sound of paper turning was heard, and Han Mengqi quickly found the location of the row.
"At that time, you will be able to graduate from me."
When he met the only person in the office, he saw that the little girl's face gradually turned red and she stammered.
"Thanks."
…
"You ask!"
[Golden reward mission starts!]
"But don't be too proud. This question is just to test whether you completed the paper yourself. The next question is the real challenge."