Chapter 30 He didn't write this randomly
"This morning I will explain to you several main aspects, including the concept of prime ideal decomposition and the solution of quadratic indeterminate equations, as well as speculations on the proof of Fermat's Last Theorem."

“If you have any questions, you can ask them during the question-and-answer session later.”

Tang Shihong was standing on the podium wearing a light blue sweater. He had taken off his coat and placed it beside him.

After briefly introducing myself, the morning lecture officially began.

At first, everyone sat up straight and paid full attention, but as the content moved from algebraic integer rings to ideal integral groups and then to solving quadratic indeterminate equations, many people began to become confused.

I seem to understand but not understand.

Especially the final Pell equation and Fermat's Last Theorem, the levels involved don't seem to be something they can grasp.

However, it did make me more aware of myself.

Although they are far ahead of their peers, they are still beginners when it comes to mathematics.

Xu Yuan had already learned a lot of mathematics when he was preparing for postgraduate studies and doctoral studies in his previous life, so he was naturally familiar with the relevant theoretical knowledge. Therefore, he actually gained a lot from listening to this academic report.

As for Professor Tang Shihong from the Department of Mathematical Sciences at Qinghua University, he is not unfamiliar to him.

The other person looked a few years older than Qi Tongxiang, but his hair was much thicker, and coupled with the advantage of a square face shape at this age, he gave off a more elegant temperament.

In his previous life, he met the other party several times after he was admitted to Qinghua Graduate School.

As a second-level full professor, he also serves as a member of the Mathematics Council and has in-depth research in the fields of number theory and differential geometry.

……

"You can see that we consider the decomposition problem on the extended ring, but there is no unique decomposition theorem on this ring."

“So the proof cannot be completed directly.”

After Tang Shihong finished talking about his speculation on the proof of Fermat's Last Theorem, he once again turned to the students and said, "Now is the question-and-answer session. Are there any students who would like to raise their hands? Feel free to ask any questions you encounter in mathematics." He kept a smile on his face while speaking, trying to appear as amiable as possible.

Unfortunately, after nearly half a minute of silence, no one raised their hand.

The main reason is that most people only have a vague understanding of the answers and cannot think of any questions that are suitable for the current situation in a short period of time.

Naturally, no one was too embarrassed to raise their hand first.

Xu Yuan looked around and saw that no one else was moving, so he had to be the first to try it out.

"Professor Tang, I have a math problem that bothers me."

"Tell me something quickly." Tang Shihong immediately locked his eyes on Xu Yuan.

His eyes were full of encouragement.

As a mathematics professor, he was invited by the Mathematics Council to host an academic report. If the lecture turned out to be too dull, he would lose face.

After all, there will be professors from other universities giving academic lectures next.

Now that we finally have a cooperative student, we must be feeling somewhat happy and delighted.

Xu Yuan didn't care what Tang Shihong was thinking, and the next second he directly told him about the problem he had not yet solved.

"Professor Tang."

"I would like to ask you for advice on proving the intervals between infinite Carmichael numbers."

As Xu Yuan finished speaking, most of the students in the room immediately showed puzzled expressions on their faces.

A huge question mark slowly appeared in my mind.

What is a Carmichael number?
Tang Shihong secretly frowned, and the good impression he had just formed disappeared in an instant.

He did not think that a student who had just participated in the finals would study the interval proof problem of Carmichael numbers. He guessed that it was probably that this student learned about it by chance and told it at this time to satisfy his vanity. The key point is that this problem has troubled the mathematics community for many years. If he could solve the proof, he would have returned to school to write a paper overnight.

As the thought remained here, Tang Shihong still maintained his smile and provided scientific knowledge to others at the same time.

"Ever since three famous mathematicians from overseas completed the proof of the infinity of Carmichael numbers nine years ago, the question of the intervals between them has remained unresolved."

“I don’t know what specific questions this student has, so you can go to the podium and write them down directly.”

He intended to put Xu Yuan in a dilemma so that he could take the opportunity to teach him a lesson and prevent him from being too ambitious in the future.

As a result, Xu Yuan stood up and walked towards the podium without saying a word without any hesitation.

Tang Shihong was stunned for a moment, then quickly came to his senses and handed a piece of chalk to Xu Yuan.

He acted as if to say, "Let's see how long you can act."

But soon as Xu Yuan continued writing, he began to lose his composure when a large number of mathematical formulas appeared on the blackboard.

"This is... the sieving method."

He couldn't help but let out a light exclamation, and his eyes widened instantly.

He never expected that Xu Yuan was actually studying Carmichael numbers and was trying to use the sieve method to prove the interval problem.

It was completely beyond his understanding of math competition students.

Just as he was still immersed in this shock, Xu Yuan's voice suddenly came to his ears again.

"I have finished writing Professor Tang. I can't continue my proof here."

Tang Shihong came back to his senses and looked at Xu Yuan with a burning gaze, as if he had discovered a treasure buried in quicksand.

After adjusting his mood a little, he did not explain immediately. Instead, he lowered his eyes, looked at the name on the camper card, and asked again.

"Student Xu Yuan, when did you come into contact with Carmichael numbers? You have been studying them for quite some time, right?"

"I discovered it by chance during the exam the day before yesterday. After finishing the test paper, I thought about studying it to kill time. I didn't expect it to be so difficult that I could only prove it to this extent." Xu Yuan thought that Tang Shihong was just asking casually, so he didn't think much about it and chose to answer truthfully.

But when these words reached Tang Shihong's ears, their power was no less than that of a blockbuster bomb.

I couldn't even believe it when I first heard it.

"You mean it took you only two days to complete these proofs? That's incredible."

Xu Yuan wanted to correct the other party that it actually took him more than three hours, but after meeting Tang Shihong's eyes at this moment, he just nodded and swallowed his words.

In the following time, Tang Shihong did not hold back and told Xu Yuan all about his previous experience in studying Carmichael numbers and the method used by overseas mathematicians to prove the infinite number of Carmichael numbers.

Finally, he took the initiative to invite Xu Yuan to study in the Department of Mathematical Sciences of Qinghua University.

As for the other contestants who were left behind by the two of them, they were confused the whole time.

There were only three questions left in my mind.

what's going on?
Why isn’t the get out of class over yet?
what am i doing?
However, the one with the biggest emotional fluctuations is undoubtedly Lin Haoming.

When he heard Xu Yuan was studying Carmichael numbers, he didn't take it too seriously. After all, math competition students all have similar problems to a greater or lesser extent.

When he first participated in mathematics competitions and achieved good results, he also tried to solve the Riemann hypothesis.

But who would have thought that they were just talking, while Xu Yuan actually proved it with actual actions, and judging from what Tang Shihong said, it seemed that this method of proof was feasible.

……

(End of this chapter)