"Erdesh's arithmetic sequence conjecture? Weren't you still studying differential equations before? Why are you starting to study number theory again?"

When Zhao Xiancai approached Professor Liu Shan and asked him about a problem he encountered while studying Erdös's arithmetic sequence conjecture, Liu Shan asked Zhao Xiancai somewhat unexpectedly.

"I accidentally saw the content of Erdős' arithmetic sequence conjecture at home during the summer vacation. I found this conjecture quite interesting, and I was also interested in this aspect of sequence before, so I tried to prove it.

Then it got stuck out of control, and now it's impossible to extricate itself.

I am now trying to prove that this conjecture applies to arithmetic triples, and then find a way to generalize this surface to arithmetic sequences of any length."

Zhao Xiancai explained to Professor Liu.

"You switched from differential equations to number theory in one summer vacation. Is your transition very fast?

This is not a good habit of yours. I know you are smart, but no matter how smart you are, it is not good to always give up halfway when doing things, and you will not achieve great things."

Liu Shan didn't say too much to Zhao Xiancai. After all, he was also experienced. He knew that there are some things that only you will know how to turn back after you hit the south wall and suffered a loss. Sometimes it is useless to suffer a loss, or even suffer multiple losses, or

It took a big loss before he knew how to turn back, so he also knew that it was useless no matter how much he said now.

Moreover, Zhao Xiancai is young now and has not yet reached his twenties. With the capital of trial and error, it is not a bad thing to learn more about and study other fields of mathematics.

If something can really come out, this is naturally the best. If it doesn't, he can change it in time.

Therefore, after saying these few words, Liu Shan seriously thought about the question Zhao Xiancai asked.

“Tsk, this question also involves combinatorial mathematics, which is a bit deep.

Although I also have some knowledge of number theory and combinatorial mathematics, I usually focus on studying the qualitative theory of differential equations. I can't solve your problem.

You go find Professor Yan, she has been studying discrete mathematics for many years.

By the way, at the end of this month, a professor from the Discrete Mathematics Research Center of Mindu University will give a report. Please pay attention and listen to it when the time comes. If you are interested, it may be helpful to your research."

After thinking for a while, Liu Shan asked Zhao Xiancai.

"Thank you Professor Liu."

Seeing that Liu Shan had no idea about this problem, Zhao Xiancai had no choice but to go to the Professor Yan he mentioned.

"Wait a minute, let me ask you if Professor Yan is in the office now. If she is, you can go directly to her. If not, then you can make an appointment with her first and then go over."

Seeing that Zhao Xiancai was about to leave, Liu Shan also stopped him and started calling the professor he said was Professor Yan.

"Hey, Professor Yan,

Yes, it’s me, Liu Shan.

A student of mine came to ask me a question about discrete mathematics in number theory. I haven't touched number theory for a long time. His question was also a bit difficult and I couldn't solve it.

So I just want her to ask you, are you in the office now?"

"Don't you teach courses like ordinary differential equations and dynamical systems? Why do you still have students asking you questions in this area? Do you teach graduate students who study number theory?"

Before answering the phone, after seeing the name Zhao Xiancai on the phone screen, Professor Yan was a little curious. She and Liu Shan were just ordinary colleagues and had little contact. They didn't even know each other.

After so many words, why did Liu Shan suddenly call him?

But now after listening to what Liu Shan said, Professor Yan became even more curious.

Liu Shan teaches both undergraduates and graduate students, but regardless of whether he teaches undergraduates or graduate students, even if these are related to discrete mathematics, the relationship is not deep, at most it is superficial.

And if it was an ordinary problem, she believed Liu Shan could solve it.

Now Liu Shan is solving problems that she doesn't understand. She estimates that they are at least the problems that graduate students encounter in the process of doing research.

But Liu Shan doesn’t have graduate students in this field. Why would graduate students studying this field come to ask him this question?

This is like asking your English teacher a math problem, there is no logic at all.

"No, the student who asked me the question is not my graduate student, he is not even a graduate student, he is an undergraduate student.

It’s the question our teacher, Zhao Xiancai, who often chats in the group chat, asked.”

Liu Shan also answered Professor Yan’s question.

"Oh, it turns out to be Zhao Xiancai.

Okay, I'm in the office now, if he has time now, you can ask him to come over now."

As soon as he heard that it was Zhao Xiancai, Professor Yan immediately understood.

Although the exempted examinations have not yet started, the application for exempted courses has already begun. Therefore, Professor Yan also knew that Zhao Xiancai had already applied for all the required professional courses and some elective professional courses after his undergraduate degree.

Moreover, last time Zhao Xiancai went to Liu Shan to ask some questions, and then published a paper in District 2. She was also very curious whether Zhao Xiancai had any new ideas this time.

"Okay, Professor Yan's office is in 203. You can go find her now."

After ending the phone call with Professor Yan, Liu Shan asked Zhao Xiancai to find Professor Yan.

And Zhao Xiancai, after saying goodbye to Liu Shan, went to find Professor Yan.

The Professor Yan Liu Shankou mentioned was named Yan Xingying, and he was engaged in research work in discrete mathematics. These were what Zhao Xiancai found after searching on the Beijing University official website when he left Liu Shan's office and went to Professor Yan's office.

Only then did I know.

"Hello, Professor Yan."

After arriving at Professor Yan Xingying's office and knocking on the door, Zhao Xiancai, who received a response, walked into the office and saw a middle-aged woman sitting at a desk.

"Are you Zhao Xiancai?"

It seems that this middle-aged woman is indeed the Professor Yan that Zhao Xiancai is looking for.

"Um……"

Zhao Xiancai nodded and was about to repeat his purpose of coming here, but Professor Yan had already spoken.

"What question are you asking?" Yan Xingying asked

Since Professor Yan was so direct, Zhao Xiancai, who came to ask the question, naturally stopped talking nonsense and directly said the question he wanted to ask.

"It is indeed about discreteness, but you can ask doctoral students to write a graduation thesis on this question. Where did you get it?"

After hearing what Zhao Xiancai said, Yan Xingying nodded and asked Zhao Xiancai very curiously.

"This is a problem I encountered when I was studying Erdös's arithmetic sequence conjecture," Zhao Xiancai answered truthfully.

"What? Erdös' arithmetic sequence conjecture? Are you studying Erdös' arithmetic sequence conjecture?"

After hearing what Zhao Xiancai said, Professor Yan immediately showed an expression of disbelief on her face. Her expression was much more exaggerated than when Professor Liu heard Zhao Xiancai say that he wanted to study the Erdős arithmetic sequence conjecture.

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