Not far away, Mei Yuqing, who had been paying attention to Pang Xuelin's movements, said strangely: "Xiao Xin, what's wrong with Xiao Lin?" ”

"I don't know." Qi Xin shook his head, and then frowned slightly, "He probably thought of any inspiration again and went back to the room to study, right?" ”

This is not the first time Pang Xuelin has done this kind of thing, there have been several times when she asked Pang Xuelin to dinner, and when the appointed time came, she found that the other party did not come at all, and when she called to ask, she learned that the other party had forgotten the time.

Even once halfway through the meal, Pang Xuelin suddenly had some inspiration, and then directly left Qi Xin and ran away alone......

Mei Yuqing naturally knew her son's temperament, glanced 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 a little and said, "Auntie, if the junior brother has any inspiration, will we disturb him when we go up?" ”

Mei Yuqing said: "Don't worry, let's go quietly, come out after two looks, just don't let him find out!" ”

Qi Xin nodded.

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

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

The tip of the pen swiped across the paper, making a swishing sound.

Mei Yuqing stood at the door and watched for a while, then quietly retreated.

"Xiao Qi, is Xiao Lin often like this?"

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

Mei Yuqing was silent for a long time before she said: "Xiao Qi, Xiao Lin, this child, has not been close to us since he was a child, plus my father and I have been busy with business outside, and there is very little communication between each other, to be honest, I am not a qualified mother, many times, I only know about Xiaolin from the media...... If you are with him in the future, please take care of him a little more and help me take good care of him, okay? ”

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

"Well, then I'm bothering you! Let's go down now, and if someone wants to find him later, you can help explain it, and don't let people disturb Xiaolin! ”

"Good!"

……

In the study, Pang Xuelin was engrossed in thinking and thinking.

He never imagined that Ponzi geometry could bridge the gap with the ABC conjecture through the Catalan conjecture, the Behrer function, and the bipartite map.

When it comes to the Catalan conjecture, let's start with the numbers 8 and 9.

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

8 and 9 are examples of a cubic number next to a square number.

Naturally, then, mathematicians ask: is there any other cubic number next to a square number?

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

Let's start with an intuitive exploration of square and cubic numbers, as they get bigger and bigger, they become more and more sparse among all positive integers.

It's like two people who don't like going out more and more, even if it's a neighbor, maybe they will take a picture at first, but then they go out less and less often, and it's less and less likely to run into each other.

Mathematicians have even guessed that even if they are not limited to squares and cubes, even if they are any number greater than 1, they will only "meet" once 8 and 9.

In rigorous mathematical language, 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 known as the Catalan conjecture.

This conjecture was proposed by a Belgian mathematician in 1844 and proved more than 100 years later in 2002 by the Romanian mathematician Preda Mihailescu by dividing the circular field into a Galohua model.

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

Just as Abel easily proved that higher-order equations cannot have root solutions through the idea of group theory.

However, if the Catalan conjecture were to be expanded, the question would be: Can any positive integer be split into the power difference or power sum of two natural numbers?

In mathematical terms, it becomes the Fermat-Catalan conjecture that has not yet been solved: a^x+b^y=c^z, 1/x+1/y+1/z=1, and only a finite number of trivial solutions.

And the ABC conjecture contains the inference of this conjecture!

……

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

First of all, the positive integer problem is transformed into a polynomial problem, mathematically, polynomials and positive integers have a magical similarity: you can do addition, subtraction, multiplication, you can also decompose factors, you can find the greatest common divisor and the least common multiple, and there is also a 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 the so-called "irreducible polynomial".

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

……

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

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

Then add the "∞" to the complex plane, and you can make up for the missing points of the spherical surface, and the so-called "Riemann sphere" can be obtained.

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

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

……

[For the spherical coverage derived from the function f(x), assuming that its coverage number is d, then saying that a point a is a branching point is equivalent to saying that f(x)=a has less than d solution values, i.e., a is a branching point if and only if f(x)=a has a heavy root.]

Take advantage of the famous Möbius transform

z↦az+bcz+d，

It is possible to move the three branching points to 0, 1, and infinity (∞), respectively, and the Möbius transform does not change the nature of spherical coverage. So, we only need to study the spherical coverage of the branching points at 0, 1, and ∞, and then we get the Bieray function! 】

……

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

Through the Catalan theorem to connect the Berey function, through the Beret function to launch the two-part map, and then connect the Ponzi geometry to form a complete logical chain!

The idea is completely opened!

Unconsciously, it was already bright outside the window, Pang Xuelin stood up and stretched.

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

That sense of transparency close to the truth keeps his nerves in a state of high excitement all the time.

Pang Xuelin looked at the time, it was already eight o'clock in the morning, and the report meeting was about to start at nine o'clock, the ideas had been opened, and it was too late to derive the specific results, so put it at the report meeting!

Pang Xuelin lowered his head and couldn't help but sigh softly.

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

When he turned around, he saw Qi Xin on the recliner in the corner of the study, sleeping deeply, still wearing the dress he wore last night, revealing his snow-white fragrant shoulders.

Qi Xin in the dream seemed to feel a little cold, and the whole person shrank into a ball.

Pang Xuelin thought about it, picked up his coat from the hanger on the side, and went over to cover her.

Unexpectedly, this move woke up Qi Xin.

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

Pang Xuelin said: "It's eight o'clock in the morning, since you wake up, go to sleep in the room!" ”

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

Pang Xuelin thought for a while and said, "That's okay, I'll go and call up for breakfast!" ”

While letting the waiter serve breakfast, Pang Xuelin also went to take a shower and change 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 is like a lecture hall of a university, which can seat two or three hundred people, and when Pang Xuelin arrived, the people had already arrived.

Pang Xuelin directly found the host of this report meeting and said: "Remove everything from the projection, I won't talk about the relevant topics of BSD conjecture today, and there are markers and whiteboards?" The more the merrier! ”

The host was slightly stunned and puzzled: "Professor Pang, what are you doing here?" ”

Pang Xuelin said: "You do what I say first, and you'll know later!" ”