The Science Fiction World of Xueba

Not far away, Mei Yuqing, who had been following Pang Xuelin's movements, asked strangely, "Xiao Xin, what's wrong with Xiao Lin?"

"I don't know." Qi Xin shook his head, then frowned slightly, "Could he have thought of some inspiration again, and went back to the room to study?"

This is not the first time that Pang Xuelin has done this kind of thing. She asked Pang Xuelin to have dinner several times. When the agreed time came, she found that the other party hadn't come at all.

There was even a time when Pang Xuelin was halfway through a meal, and suddenly he had some inspiration, and then he left Qi Xin directly, and ran away by himself...

Mei Yuqing naturally also knew her son's temper, so she looked at Qi Xin and said, "It's very possible!"

Mei Yuqing said: "Xiao Qi, why don't you take me to your room to have a look..."

Qi Xin hesitated and said, "Auntie, if the junior has any inspiration, will we disturb him by going up?"

Mei Yuqing said: "Don't worry, let's go quietly, just take a look and come out, just don't let him find out!"

Qi Xin just nodded.

The two quietly went upstairs and entered the presidential suite. Mei Yuqing was obviously satisfied with her son's living environment, so after walking around, she followed Qi Xin through the living room to the door of the study.

In the study, Pang Xuelin was writing something at his desk.

The tip of the pen scratched the manuscript paper, making a swish, swish, swish sound.

Mei Yuqing stood at the door watching for a while, then quietly retreated out.

"Xiao Qi, does Xiao Lin often do this?"

Qi Xin said: "Occasionally, he used to stay up late at night, but after getting up early every day to run with me, he rarely stayed up late."

Mei Yuqing was silent for a long time before she said: "Xiao Qi, Xiao Lin has not been close to us since he was a child. In addition, his father and I have been busy with business outside, and we rarely communicate with each other. To be honest, I am not a qualified Mother, most of the time, I only know the news about Xiao Lin from the media... If you are with him in the future, please take care of him and help me take good care of him, okay?"

Qi Xin understood the meaning behind Mei Yuqing's words, nodded and said: "Auntie, don't worry, as long as I am by my side, I will definitely take good care of him."

"Well, I'll trouble you! Let's go down now. If someone wants to find him later, you can help explain it. Don't let people disturb Xiaolin!"

"good!"

...

In the study, Pang Xuelin was engrossed in thinking.

He never thought that Ponzi geometry can build a bridge with the ABC conjecture through the Catalan conjecture, the Bely function and the bipartite map.

When it comes to the Catalan conjecture, we must start with the two numbers 8 and 9.

In the eyes of mathematicians, these two numbers are unusual: 9 is 1 greater than 8, 8 is a cubic number, it is the cube of 2, and 9 is a square number, it is the square of 3.

8 and 9, is an example of a cube next to a square.

Then, mathematicians will naturally ask: Is there any other cubic number that is next to a square number?

Or in the language of mathematics, for the equation x^2?y^3=1, besides x=3, y=2, is there any other positive integer solution?

Let's explore intuitively first, square numbers and cubic numbers, when they get bigger and bigger, they will become more and more sparse among all positive integers.

It's like two people who don't like to go out more and more. Even if they are neighbors, they may meet each other at first, but then they go out less and less, and it becomes less and less likely to meet each other.

Mathematicians even speculate that, even if they are not limited to square numbers and cubic numbers, even if they are any powers greater than 1, they only "meet" 8 and 9 this time.

In rigorous mathematical language, it is the equation x^a?y^b=1,

Under the condition that a and b are greater than 1, there is only one set of solutions, that is, x=3, a=2, y=2, b=3.

This is the famous Catalan conjecture.

This conjecture was proposed by a Belgian mathematician in 1844, and was proved by the Romanian mathematician Preda Mihailescu in 2002 through the method of dividing the circle field and the Galois module.

But in fact, this conjecture can be easily proved through Ponzi geometry theory.

Just like Abel used the idea of ​​group theory to easily prove that high-order equations cannot have root solutions.

However, if we expand the Catalan conjecture, we will ask this question: Can any positive integer be divided into the power difference or power sum of two natural numbers?

Expressed in mathematical language, it becomes the unresolved Fermat-Catalan conjecture: a^x+b^y=c^z, 1/x+1/y+1/z=1, there are only finite trivial solution.

And the ABC conjecture contains the deduction of this conjecture!

...

[If you want to prove the ABC conjecture, you must first prove the Fermat-Catalan conjecture!

First of all, the problem of positive integers is transformed into a polynomial problem. In mathematics, polynomials have a magical similarity with positive integers: they can be added, subtracted, multiplied, and factors can also be decomposed. Unique Decomposition Theorem: Positive integers can be uniquely decomposed into the product of prime numbers, and polynomials can also be uniquely decomposed into the product of so-called "irreducible polynomials".

Basically, many studies on the properties of positive integers in number theory can be directly transferred to polynomials. 】

...

[For a certain positive integer k, suppose there are two coprime polynomials P, Q, where the degree of P is 3k, and the degree of Q is 2k.

The complex plane composed of complex numbers is a spherical surface, and the complex plane can be transformed into a spherical surface with only one missing point through the stereographic projection method.

Then add "∞" to the complex plane to fill in the missing points of the spherical surface, and the so-called "Riemann sphere" is obtained.

And the rational function on the Riemann sphere, that is, the quotient of two polynomials, is actually a spherical cover.

By studying the properties of the covering of a sphere, mathematicians can indirectly know the properties of the corresponding rational functions. 】

...

[For the spherical coverage induced by the function f(x), assuming that its coverage times are d, then saying that a certain point a is a branch point is equivalent to saying that the solution value of the equation f(x)=a is less than d , that is, a is a branch point if and only if f(x)=a has multiple roots.

Using the well-known Möbius transformation

z?az+bcz+d,

The three branch points can be moved to 0, 1, and the point at infinity (∞) without the Möbius transformation changing the essence of the spherical coverage. Therefore, we only need to study the spherical coverage of the branch points at 0, 1 and ∞ respectively, so that we get the Beley function! 】

...

Time passed by, and unconsciously, Pang Xuelin's eyes became brighter and his thinking became more and more transparent.

The Bely function is connected through Catalan's theorem, the bipartite map is derived through the Bely function, and then Ponzi geometry is connected to form a complete logic chain!

The idea is completely cleared up!

Before he knew it, the sky was bright outside the window, Pang Xuelin stood up and stretched himself.

Although the high-intensity thinking made Pang Xuelin feel a little tired, but he didn't feel much sleepy.

The sense of transparency close to the truth keeps his nerves in a high state of excitement,

Pang Xuelin looked at the time. It was already eight o'clock in the morning, and the report meeting at nine o'clock was about to start. The train of thought had been cleared up, and it was too late for specific derivations, so let's put it in the report meeting!

Pang Xuelin lowered his head and couldn't help but let out a little surprise.

The desk was full of manuscript paper, and a cup of coffee was placed next to it at some point, but the steaming coffee had completely cooled down.

He turned around, and saw Qi Xin sleeping soundly on the recliner in the corner of the study, still wearing the dress from last night, showing her snow-white shoulders.

Qi Xin in the dream seemed to feel a little cold, and she curled up into a ball.

Pang Xuelin thought for a while, picked up the coat from the hanger at the side, and went over to cover her.

Unexpectedly, this movement woke Qi Xin up.

The girl opened her eyes in a daze, rubbed her eyes and said, "Student, what time is it?"

Pang Xuelin said: "It's eight o'clock in the morning, since you're awake, go to sleep in your room!"

Qi Xin was taken aback, and quickly got up and said: "Don't sleep, the report meeting is about to start, I'm going to take a shower and change clothes, and we'll go downstairs together later!"

Pang Xuelin thought for a while and said, "That's fine, I'll go and get breakfast!"

While asking the waiter to serve breakfast, Pang Xuelin also went to take a shower and changed clothes, and then came to the restaurant, where the hotel had prepared an exquisite French breakfast for them.

After eating, the two went directly to the conference hall of the hotel.

The entire conference hall was like a lecture theater in a university, and it could seat two to three hundred people. When Pang Xuelin arrived, it was almost full.

Pang Xuelin directly found the host of this report meeting, and said: "Remove all the projections. Today I will not talk about BSD conjecture related topics. Do you have markers and whiteboards? The more the better!"

The host was slightly taken aback, and asked in confusion, "Professor Pang, what are you doing?"

Pang Xuelin said: "Do as I tell you first, and you will know later!"