Chapter 719： Invitation from MIT

"The answer to this question is n(2n+1)?"

Zhang Lei's eyes widened, and he followed Lu Zhou's derivation, and it seemed that he was right...

How long has it been since Lu Zhou walked up from the question mark!

I can't help but feel a sense of frustration in my heart, it's too shocking!

Professor Stephen was not surprised by Lu Zhou's performance. After all, it was Chen Ke who compared his talent with Tao Zhexuan.

"The answer is indeed n(2n+1)."

Seeing that Lu Zhou was about to return to his position, Professor Stephen shouted.

"Lu, I have another topic here, I don't know if you are interested."

Hearing the question, Lu Zhou's eyes lit up, he turned around and asked, "What question?"

"I heard from Chen that you have some research on Diophantine equations?" Stephen smiled, walked up to the podium while speaking, and picked up the chalk.

"Then I'll give you a 'simple' Diophantine equation."

Lu Zhou was just one meter in front of the podium, his eyes fixed on the blackboard.

[How to calculate a set of integer solutions for x3+y3+z3=33? 】

Lu Zhou's face gradually became solemn.

There are many math problems that seem simple, but the problems often have very complex solutions.

For example, this question from Professor Stephen is like this.

Except for Lu Zhou, the other seven students of Guanghua University were all confused, only Zheng Tianyu looked at the title and felt that he had seen it somewhere, but he couldn't remember it for a while.

Zhang Lei scratched his hair, his face sluggish.

"Is this really the answer???"

It was simply powerless to complain, Zhang Lei only felt his scalp tingling.

Look at my friend Zheng Tianyu, who is also very dazed.

Not to mention others without names.

Professor Stephen, who took everyone's facial changes into his eyeballs, looked calm and looked at Lu Zhou curiously.

He wanted to know, can Lu Zhou solve this problem?

Lu Zhou frowned, the difficulty of this question was beyond his expectations.

And he also recognized the topic that Professor Stephen posed.

This has to be traced back to the equation [x3+y3+z3=3].

Many people will definitely think of the integer solution [1, 1, 1]. In fact, there is a second group of integer solutions, which is [4, 4, -5].

But will there be a third set of integer solutions?

In 1953, mathematician louismordell raised such a question.

Interestingly, this seemingly untechnical problem has plagued the mathematics community for a long time, and it has not been solved until today.

In 1992, another mathematician rogerheath-brown proposed a conjecture when studying the zero-point density problem of the weak approximation principle failure form x3+y3+z3=kw3: for any positive number k?±4 (mod9), The Diophantine equation k=x3+y3+z3 has infinitely many integer solutions (x, y, z).

[If you have not studied elementary number theory, take k?±4 (mod9) as k≠9n+4, that is, k≠9n+4 or k≠9n+5]

Every k has infinitely many sets of integer solutions.

In the current mathematics community, when k is less than 100, except for the third group of integer solutions with k=3, only k=33 and 42 have not found an integer solution.

A problem that has not been solved in the mathematics community was taken out by Professor Stephen as an exam question.

Lu Zhou really wanted to ask the other party: Professor, do you know the answer?

He didn't say anything, but he was very excited.

A problem that has stumped the global mathematics community for decades.

Wouldn't it be cool if... he solved it?

Lu Zhou concentrated on looking at the question, and his brain began to run wildly.

First of all, we must understand why there is a condition of k? ±4 (mod9) in the conjecture of the mathematician heath-brown.

It is known that any integer can be written in one of the following three forms, 3k, 3k-1, 3k+1, and then calculate their cubes separately:

(3k)3=27k3

(3k-1)3=27k3-27k2+9k-1

(3k+1)3=27k3+27k2+9k+1

The remainders of the three divisible by 9 are 0, -1, 1, respectively, so for any integer x, there is x3≡0, ±1 (mod9).

According to the basic properties of the congruence operation, ... (omitted) ... It can be seen that when k≡±4(mod9), there is no integer solution to the equation.

Therefore, when solving the equation k=x3+y3+z3, there is no need to consider the case of k≠9n+4 or k≠9n+5.

Lu Zhou continued to think, and the classroom fell into silence.

Zheng Tianyu, Zhang Lei and other 7 students are scratching their heads, this question is beyond the outline!

Professor Stephen also just stood by and watched without saying a word.

The only hope for solving this problem lies in Lu Zhou.

A few minutes passed, and it was less than 10 minutes before get out of class ended.

Lu Zhou suddenly moved!

He walked to the podium, picked up chalk and kept writing.

[assumex3+y3+z3=k＞0, |x|＞|y|＞|z|≥√k, k≡±3(mod9) cubefree.]

[k-z3=x3+y3=(x+y)(x2-xy+y2)]

【defined:=|x+y|sothatzisacuberootofkmodulod.】

[{x, y}={sgn(k-z3)/2(d±√4|k-z3|-d3)/3d}…]

(Writing in English is because the author is too lazy to translate...)

Lu Zhou's thoughts didn't seem to be interrupted, and the chalk became less and less.

In addition to the conventional projection screens, MIT classrooms have three blackboards on the left, middle and right.

And the blackboard on the left has been slowly filled by Lu Zhou's formula derivation.

At first, Professor Stephen was relieved to see Lu Zhou's problem-solving ideas, but what he didn't expect was that the more he looked behind him, the more shocked he became.

"This..." Stephen opened his mouth slightly and wriggled for a while, "Isn't it really possible to untie it?"

What a joke, this problem is a problem that has plagued the mathematics community for decades, and will it be solved by an undergraduate student?

God, today is not April Fool's Day.

As for Zhang Lei, Zheng Tianyu and others, they have already been petrified.

I can still understand a little bit in front, but it starts to struggle a little bit later, and I can't understand it at all after that.

How do you feel that the gap between Lu Zhou and them is getting bigger and bigger?

After class ended at 12 o'clock, Lu Zhou continued to write, Professor Stephen and the rest of the classmates watched quietly.

But at this time, a figure appeared at the door.

A twenty-five- or six-year-old youth, wearing a white printed T-shirt, jeans, and short hair, looked very handsome.

The young man wanted to shout, but after walking to the door of the classroom and noticing the situation inside, he closed his mouth and walked to Professor Stephen's side, and then asked in a low voice, "Professor Stephen, is this get out of class not over yet?"

Of course Stephen knew each other. As a fellow student and friend of a proud student he was no stranger to this Cao Lihao.

"Be quiet, don't talk."

Cao Lihao shrugged helplessly, so he could only look at Lu Zhou on the podium.

After nearly an hour.

The three blackboards in the classroom have few blank spaces and are full of formula symbols.

Lu Zhou put down the chalk, looked up at the blackboard, and showed unwillingness in his eyes.

"Still can't figure it out."

Professor Stephen stepped forward with joy, grabbed Lu Zhou's hands, and said excitedly:

"Lu, on behalf of MIT, I welcome you to join us!"

ps: Sorry for not updating Chapter 2 yesterday.

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