After taking the advice, I became a top student.

At 9 PM, Chen Mo started his live stream again.

This time, he was learning math via live stream.

He has now studied far beyond the scope of high school mathematics. He has completed all of "Advanced Mathematics" and has also made progress in "Mathematical Analysis." He has a good grasp of ordinary differential equations and partial differential equations and is now studying complex analysis.

These things are naturally incomprehensible to netizens, but that doesn't stop them from enjoying the spectacle.

[Hey host, how did your exam go yesterday? When will you post your scores?]

[Haha, you're really hitting a nerve! It's fine for a streamer to just pretend online, but you're actually sending him to participate in a math competition?]

[Dude, I actually ran into the streamer at the Polytechnic University yesterday. Even though he's from No. 1 High School, he was surrounded by top students from No. 4, No. 7, and No. 9 High Schools. I think the streamer is really something.]

Yes, I can testify that I am a top student at No. 7 Middle School.

I can also testify that I sat on the same stool as the top student from No. 7 Middle School.

[Hey upstairs, did you see the class beauty?]

[I didn't see the class beauty, but the streamer was accompanied by two girls who were also considered class beauties.]

Chen Mo was engrossed in his studies, while netizens entertained themselves in the live stream, chatting happily.

On the other side, Shen Qingyi's heart skipped a beat. She had just been resting after studying and was checking Chen Mo's live stream when she unexpectedly saw such explosive news.

"Two pretty young ladies?"

"Who is it?"

Shen Qingyi felt a surge of nervousness.

How do you know she's not the class beauty?

[What the host said]

But the next moment, upon seeing the replies in the comments, Shen Qingyi's face instantly brightened, and a radiant smile appeared.

"Could you explain this problem to me?"

Seeing that it was almost time, Shen Qingyi put away her phone, took the draft paper, and went to Chen Mo's side.

[The class beauty has arrived!]

[Can the class beauty show her face? I'll buy you a sports car.]

[You're living in such a depressing atmosphere upstairs!]

"What's wrong? Is there something on my face?"

Shen Qingyi asked curiously, then looked down to check if there was anything wrong with her.

"Are you having such a good time today?"

Chen Mo asked with a smile. He noticed that when Shen Qingyi came to ask questions today, she had a sweet smile on her face the whole time, and her two shallow dimples were simply adorable.

"Is it wrong to think about happy things?"

Shen Qingyi returned with an air of arrogance.

"sure."

Chen Mo didn't ask any more questions and looked at the question that Shen Qingyi handed him.

Wow, did you guys notice? When the streamer looked at the class beauty, he couldn't hide his smile. I know all too well that kind of genuine happiness.

There's a story upstairs.

Unfortunately, we didn't go to the same university after graduation; long-distance relationships don't last.

So sweet, I'm totally shipping them!

"Number theory?"

After reading the question, Chen Mo turned back to look at Shen Qingyi with some surprise. Generally speaking, number theory is not tested in the college entrance examination, and even if it is, the questions are very simple.

Shen Qingyi nodded, "I'm currently studying for competitions on my own, preparing to compete next year."

"Focusing on the college entrance exam is a good thing."

Chen Mo advised, "With your grades, as long as you keep it up, you can easily choose any university in China."

"Never mind that, just explain the problem to me. How did you suddenly think of using Pell's equation here?"

Shen Qingyi shook her head.

She didn't tell Chen Mo that the reason she wanted to participate in the competition was so that she could spend more time with Chen Mo. She absolutely had no intention of dating early, but for some reason, studying with Chen Mo made her feel very happy.

It would be really interesting to go to other schools, to Beijing, or even to compete abroad with Chen Mo in the future!

Since Shen Qingyi had made up her mind, Chen Mo said no more and looked at the question.

……

Beijing, Yanbei University School of Mathematics

Zheng Mingyang stared at the equation before him, his eyes bloodshot.

He originally thought that proving an equation that a high school student had casually written would be a piece of cake.

Unexpectedly, after staying up for two consecutive nights, he became increasingly confused.

He tried to derive it using standard Gaussian sum theory, but found that the classic Gaussian sum is a quadratic form of ∑_k=1^{q}e^{2πik²/q}, while the exponent in the invariant of the provincial competition paper is linear e^{πik/q} and has the characteristic χ(k).

When χ is a principal eigenvalue, ∑_k=1^{q}e^{πik/q}=∑_k=1^{q}(−1)k, which is obviously 0 or -1. This is not equal to √q multiplied by a constant unless q is specially restricted.

When χ is a non-principal eigenvalue, this sum is a Gaussian sum, but in classical theory its modulus is √q, and the specific value depends on some sign within the square root of χ, and there is no simple closed form.

In other words, the constant equation does not always hold; it only holds for certain specific q and χ.

What he needs to solve now is: under what conditions does this equality hold? And how can he prove it?

This problem had been bothering it for two days, but it had no clue how to solve it.

"Old Zheng."

Zhao Yiming walked briskly into the office, intending to check on his old friend's certificate, but he only saw Zheng Mingyang looking haggard and exhausted.

He understood what had happened. When he was young, he often stayed up all night to prove something. He used to have a thick, black head of hair, but now it had become oily and shiny from staying up all night.

Besides, they are no longer young, how can they keep staying up so late?

"Old Zheng, don't keep thinking about it to yourself. Since that candidate wrote this equation, let's just go and ask him."

Zhao Yiming offered some words of advice.

Zheng Mingyang, however, was unconvinced. "How could a high school freshman understand Gauss better than me?"

"It wouldn't hurt to ask."

Zhao Yiming continued to persuade him.

Zheng Mingyang didn't persist. He was indeed stuck in a bottleneck, and he knew that his state of mind was not right. However, because of the thesis, his mentality was a bit off, which is why he was still staying up all night to work on it at this age.

He definitely needs external help to overcome his inner demons.

Going to see that little guy might be a good option.

Of course, he didn't expect the kid to be able to provide proof. If the kid really knew how to prove it, he would have given it to him during the exam, instead of waiting until now.

But if that little guy can provide him with some inspiration, that would be good too.

He still had high hopes for the kid's talent; when it comes to mathematics, talent is key.

Zhao Yiming immediately took out his phone and dialed the number of the president of the Chengdu Mathematical Society.

"Old Li, you haven't rested yet, have you?"

The call connected, and Zhao Yiming asked warmly.

"I'm still at the math club. I've been so busy these past few days, how can I possibly rest at this hour?"

A bitter laugh came from the microphone.

The president of the Chengdu Mathematical Society had also spent some time at Yanbei University, and the two were old friends, so there wasn't much pretense between them.

"There's something I'd like to ask you for a favor."

"What kind of help? You guys have really helped us a lot this time. Tell me, if I can help, I definitely will."

Li Huachun said with great enthusiasm.

Zhao Yiming didn't stand on ceremony. "I have a test paper here. I've sent you the number via WeChat. I want to know who the examinee is."

"This...this is against the rules."

The voice on the other end of the microphone immediately became hesitant and stammering.