In 1922, the British mathematician Modell proposed a famous conjecture, which is called the Modell conjecture by the habitual naming method. In its original form, the conjecture was that any irreducible, rational coefficient binary polynomial would have a finite number of solutions at most when its "deficit" was greater than or equal to 2. Keeping this polynomial as f(x,y), the conjecture shows that there is at most a finite logarithmic even xi,yi∈Q such that f(xi,yi)=0.

Later, the conjecture was extended to polynomials defined on any number field, and with the advent of abstract algebraic geometry, algebraic curves were used to describe this conjecture again. Thus, what Model's conjecture actually proves is that an algebraic curve with a deficit greater than or equal to 2 is at most a finite number of K points arbitrarily defined in the number field K.

In Fermat's theorem, Fermat's polynomial x^n+y^n-1 has no singularity, and its deficit is (n-1)(n-2)/2.When n≥4, Fermat's polynomial satisfies the conjecture condition. Therefore, xn+yn=zn has at most a finite number of integer solutions. That is, when n > 2 (n is an integer), there is only a finite set of coprime a,b,c such that a^n+b^n=c*n. This was produced during the proof of Fermat's theorem, which was proved by the famous mathematician Faltins in 1983.

However, in the process of proofing Modell's law, it does not only involve the knowledge of simple number theory, but also uses a lot of algebraic geometry knowledge such as Shavaralwich's conjecture, Jacobian cluster, high, homology and's conjecture in the proof process. At the same time, the Modell conjecture is not only used to prove Fermat's theorem, but also has many other uses.

When Junxin first proved the first question of the additional question of the test paper, the number theory question, he began to think of the Moder conjecture, one of the two most important conjectures before the successful process of proving Fermat's theorem.

In this way, in this quiet classroom, Junxin kept writing on the paper alone. Mathematics is not a subject that you can completely copy if you know the answer, but requires you to be able to deeply understand the thinking problems in the process of solving it, and this is often the place where mathematicians pay the most attention. Mathematics has developed to the present day, divided into n many branches, and only a very few or even non-existent mathematicians can be proficient in all branches, so the ideas and ideas involved in solving a certain problem are the most important, because this is often breakthrough thinking, which often brings some inspiration to mathematicians when studying their own problems. In the eyes of mathematicians, there really is nothing more important than this.

"Lao Liu, what do you think of this test paper?" After completing the marking, Professor Chen took out one of the test papers and said to Professor Liu.

"I have also read this test paper, although the steps are not very detailed when answering the questions, but the thinking is very clear, there is nothing to doubt!" Professor Liu said.

"Listen to Xiao Wang, this candidate only took the test for thirty minutes?"

"Well, the test paper is produced by us together, so you and I know the difficulty of the questions on the test paper, even if a junior student does it, it is impossible to completely guarantee that he will get all these 22 questions right in three hours, let alone a freshman who has just entered the school? So this time, there is a genius among the freshmen! "Professor Liu's paintings are quite emotional and incredulous.

"Hehe, that's a good idea, I just have a freshman class this semester, so I can go and see what kind of person this genius is!" Professor Chen said with a smile.

"You're fine, it's a pity that I'm going to teach a sophomore course, and there is no freshman, otherwise I can take a closer look at this genius's ability!" There was a sense of jealousy in Professor Liu's language. "By the way, didn't you approve of Commissar Hu's idea at that time? Now, Committee member Hu's view is obviously valid, what do you say? ”

Professor Chen laughed and said, "This shows that there is still such a long distance between me and the members of the department!" ”

"Report!" The two were talking and laughing, when one suddenly reported loudly outside the door.

Professor Liu and Professor Chen glanced at each other, and Professor Liu spoke, "What's the matter?" ”

I saw one person push the door in, it was Professor Hu's assistant, the assistant first greeted the two of them, and then said: "The people from the dormitory class came to me just now and asked me, have any students been called by the two professors?" ”

"What's going on?" Professor Chen asked curiously, "The school has just started, the military training has not yet begun, and we haven't had a single class, who can we know?" Naturally, no one was called! ”

"It's a freshman named Junxin.,When the dormitory department just checked the room.,Found that Junxin wasn't in the dormitory.,Asked the three people in the same dormitory.,The three of them said that Junxin left the examination room directly after the exam.,The three of them haven't seen him either.,It's estimated that he was called by a professor.。 So the dormitory department just came to ask me, and I came over to report to Leader Liang Wen! ”

"We haven't called anyone, so ask the others! Junxin, Junxin, why is this name a little familiar? Professor Liu muttered twice and said with a little doubt.

"Lao Liu, didn't you mention him just now? It's a perfect score of 30 points! Professor Chen reminded on the side.

"Oh, it's him?" Professor Liu said suddenly, and then said to the assistant, "You also follow and look for it, I guess where you stayed and forgot the time!" ”

"Yes!"

Professor Mizuki generally does not manage the affairs of students' lives very strictly, so he did not pay attention to this matter, and Professor Liu quickly put this matter in the back of his mind and continued to discuss it with Professor Chen.

The campus of Mizuki University is still very large, and it is so difficult to find a person who may not return home at night by relying on three or five people in this small campus, and in the end, in desperation, the dormitory department can only be reported to the senior management of Mizuki University layer by layer.

Mizuki University is very strict with the management of students, and the requirements for work and rest time are naturally the same, so as soon as I heard that some new students did not return home at night, the school management of the logistics department immediately notified the counselor. Due to the very backward personal communication technology in the 80s, even if the counselor knew about it, there was no way to find Junxin immediately. You can only look for it slowly from place to place on campus.

Time passed little by little, until the specified time, several people got together, still did not find Junxin's figure, the counselor glanced at his watch, the time had pointed to half past twelve in the middle of the night, couldn't help but smile bitterly, and said to Professor Liu's teaching assistant: "It seems that the first freshman of our Shuimu University who does not return at night is going to be born in my hands!" ”

The teaching assistant sympathized with it, and the school in the 80s still looked at things like making mistakes more seriously, so although Junxin was a freshman and a freshman who had just started school, there was still a copy of such a mistake of not returning home at night to be hung up on the instructor's side in the end. In this way, the counselor will definitely not be able to score any good grades in the evaluation at the end of the semester.

"Why don't you look for it again?" The teaching assistant whispered a suggestion, but there was no hope in his heart.

"What are you looking for, it's already half past twelve, and the dormitory should be locked, even if you find it, what can you do?" The counselor said bitterly, "Go back, military training will start tomorrow morning, and you can't delay the entire class for him alone!" ”

"Okay!" The teaching assistant thought about it and agreed with the counselor. After all, he is only here to help, and he is not a guide himself, so there is no need to spend half a day for a person he has never met.

"Excuse me, tonight. Go back and thank Professor Liu for me! The counselor waved his hand weakly. The counselor's surname is Bao, called Bao Yue, and the legend is that he is the seventy-first grandson of Bao Zheng, although I don't know if it's true, but judging from his dark skin and upright personality, the possibility is still very large. But now this upright descendant of Bao Gong has also been completely lost his temper by Junxin's unreasonable behavior, and there is only the idea of concocting it ruthlessly after finding Junxin.

At this time, Junxin, who was still in the remote all-night study room, naturally did not know that he had been successfully "remembered" by the counselor, and at this time he had completely forgotten the time and devoted himself to the proof of Modell's conjecture.