I cheated once and became addicted. I feel that my brain is better than anything else. Really, who would want to spend several times the time and effort with that kind of brain.

Talent determines the upper limit, and hard work determines the lower limit. Talent can sometimes determine a lot of things, which can save a lot of time in memorizing and understanding, giving people more time to think about the root causes, such as in mathematics, what are the essences of many formulas and theorems.

However, Li Xuan thought to himself that he could not be blamed for wanting to cheat. No one wanted to waste his life. Time is so precious and hard work is meaningless if it is not for success. He did not believe that "success does not matter, as long as you enjoy the process."

"Such nonsense.

"System, you have to dress in women's clothing to be appreciated, right?"

Li Xuan confirmed again.

System: [The host who does not dress as a woman and is not beautiful enough will not be able to gain appreciation points.]

"Okay, I'm convinced."

Li Xuan was a little helpless.

He thought about his experience at the last English Festival. Would Lingchu call him a woman again? Otherwise, he could just take the initiative to ask Lingchu to go out in women's clothing. That way he could gain a lot of appreciation and not be recognized by the people around him.

However, if we consider efficiency and consider it as a long-term career in the future, live broadcasting of women's clothing seems to be the right way, so that we can gain more appreciation value. After all, it was because the video was circulated on the Internet last time that we had so much appreciation value. Now I enjoy it

The value also increased slightly, also because the video was circulated online.

It's just... I always feel like something is wrong.

wrong!

When did he stop resisting women's clothing?

Li Xuan suddenly realized, his heart felt so cold, Xuan, why have you changed?

…

…

Ignoring the matter of women's clothing, Li Xuan's main idea in the afternoon was to continue studying number theory.

The first test of the National High School Mathematics League does not test number theory, but number theory is only tested in the second test. Number theory also appears as a big question, with extremely heavy points, and is generally a difficult question. Combination and number theory are generally difficult questions, which are very difficult for ordinary contestants.

Difficult to make.

For experts, plane geometry is a question that cannot lose points. The difficulty of algebra questions is not necessarily different. It may be difficult or very simple, depending on luck. If you just want to get a National Level 1 exam, two or more questions in the second test will be enough.

But Li Xuan plans to definitely enter the provincial team, so he must not lose the number theory points in the second test easily.

Now that Li Xuan is very strong in plane geometry, it is necessary to start studying elementary number theory seriously. The content starts from Euler's theorem, Sun Tzu's theorem, Euclidean division, infinite descent method, grid points and properties...

Like the college entrance examination, the high school mathematics league also has an exam syllabus. The knowledge required for the exam will not exceed the scope of the syllabus and focuses on test skills.

While Li Xuan was reading, other students were also reading and doing questions, and the classroom was quiet.

Liang Zhihui walked towards Li Xuan with the book in hand, sat next to Li Xuan, and pointed at the question: "Li Xuan, I have a question that I would like to ask you. Is it convenient for you?"

In the entire competition class, Liang Zhihui could only ask Li Xuan questions, and he only admitted that he was inferior to Li Xuan in mathematics.

Li Xuan was startled for a moment, then turned to look at the question, "What's the problem with this question?"

Liang Zhihui said: "The answer is omitted, I can't think of it."

Li Xuan looked down and nodded, "Well... you may think the problem is too complicated. Think about it simply. Don't think about it as a whole. From the perspective of local prime factors, you actually need to prove that the divisibility relationship is true. Just prove

The exponent of any prime factor in the dividend is no less than the exponent in the divisor."

Liang Zhihui looked at the title and remained silent, frowning in thought.

When he has no clue when facing a mathematical problem, Li Xuan can always grasp a clear and simple way of solving the problem, which is more like an intuition. This is not the first time that he has asked Li Xuan a question, nor is it the first time that he has asked Li Xuan a question.

Once I was shocked by Li Xuan's ability to solve problems quickly.

In the past, he would not ask Li Xuan questions, always feeling subtly dissatisfied, but after asking him a few times, he felt more and more that he was not as good as Li Xuan.

There is nothing to be depressed about now. I think I am incomparable. Why should I be jealous to make myself ugly?

Without Li Xuan, he would still be no match for a mathematical genius like Ouyang Zhe. On the contrary, Li Xuan's existence could always remind him of his shortcomings. With Li Xuan by his side, he could urge himself to work hard.

There are only six people who have the strength to enter the national team. He is far from reaching this strength now, but as long as he keeps surpassing himself, sooner or later he will find his own glory.

Regarding this question, Liang Zhihui still couldn't figure it out, "I still don't understand it very well. According to the idea you mentioned, how do you prove it?"

Li Xuan blinked and pointed to the combinatorial number in the question, "In this question, any prime factor in the divisor can be obtained using Lucas' theorem. There is a proof process for this theorem in "Elementary Number Theory". This Lucas theorem

It is very useful to solve the problem of modulus of large combination numbers. It is used to find the value of c(n,m) mod p. By the way, p here must be a prime number. You see, it just meets the meaning of the question."

Liang Zhihui suddenly remembered something, "Lucas' theorem? Is this an example question on page 40 of "Elementary Number Theory"?"

Li Xuan smiled and said, "Yes, I just saw it, but I didn't expect it to be used in your question."

Liang Zhihui was a little confused.

Knowing the theorem and applying the theorem are completely different things. Lucas's theorem is not required to be mastered, but only understood. Li Xuan knows how to apply the theorem after seeing it. When it comes to more complex examples, he undoubtedly has a deep understanding of Lucas' theorem.

…

When Liang Zhihui saw this question, he never thought about Lucas' theorem, otherwise he would not have been stuck for so long. It is not difficult to follow Li Xuan's ideas, but without Li Xuan, he has no ideas and does not need to

After taking the exam, I saw that I was not as good as Li Xuan.

Liang Zhihui sighed. Once he had an idea, he didn't bother Li Xuan. He picked up the topic and studied it by himself. He didn't need anyone to teach him every step. Li Xuan gave him some inspiration and he could do it.

This method of asking questions is also more effective in promoting his progress.

But at this moment, Liang Zhihui still had a strange feeling in his heart, that is, was Li Xuan solving problems faster and faster? Li Xuan just took a few glances and caught the idea. Or to put it more simply, Li Xuan was solving problems faster and faster.

Xuan seems to be getting smarter and smarter.

This is a bit incredible.

Could it be that Li Xuan's talent is not only in plane geometry, but also in number theory? He took a deep breath, and in addition to admiration, he also felt a bit of unspeakable envy.

…

…

After class in the evening, Li Xuan picked up his cell phone and looked at it. He still didn't receive a call from his sister, and he felt a little worried for some reason.

In the classroom, classmate Jiang Shu suddenly shouted:

"I feel like I might be a genius in number theory! I proved the world-ending problem, the twin prime number conjecture, and the infinity of twin prime numbers."

The classmates were all stunned, their eyes full of disbelief. They ran to Jiang Shu's side and asked classmates to pass over. Many of them wanted to see the joke.

"Really or not?"

"Proved the world's difficult problem?"

"Take it and see!"

…

When Li Xuan saw the movement, he was a little speechless and pretended not to hear it.

It turns out that he had just heard about these conjectures in number theory, and he didn't believe them and wanted to prove them. Later he had to admit that the proofs were too complicated and he couldn't do it now. If high school students can prove that the twin prime numbers are infinite, then there will be so many mathematical problems in human history.

The house is probably in ruins.

"Everyone, step aside. I'll let Li Xuan take a look. Isn't Li Xuan the best at mathematics?" At this time, Jiang Shu took the initiative to find Li Xuan and put the proof process on Li Xuan's desk, "Li Xuan, look at my

Can you prove it?"

The classmates also came to watch and join in the fun.

Li Xuan looked down helplessly and saw Jiang Shu's proof paper, and was speechless for a moment.

Jiang Shu’s proof of infinite twin prime numbers is simply as follows:

Let n=2*3*5*7...*p (p is a prime number), then n+1 and n-1 are twin prime numbers. The larger p is, the larger n is, because the prime numbers are infinite, so the twin prime numbers are infinite.

Jiang Shu smiled and said: "My proof is very subtle... I admit that your geometry and algebra are very strong, but number theory is most about talent, and my talent seems to be okay."

Li Xuan just glanced at it casually and saw too many things worth complaining about. He didn't know how to complain at the moment. Seeing Jiang Shu was in high spirits, he couldn't bear to hit him, "Well, this is actually a bit problematic...forget it, you are happy.

That’s fine.”

On such a world-wide problem, when you see other people's wrong proofs and nonsense logic, why do you have a strange feeling that science has been tainted? Anyway, if Euclid saw his method of proving the infinite prime numbers and used it like this, he would definitely be on the coffin board.

Can't cover it anymore.

Liang Zhihui frowned as he watched, not believing that Jiang Shu could prove the twin prime conjecture. Jiang Shu liked to use crooked methods to solve problems. He knew it.

In this class, he allows Li Xuan to be better than him, but he does not allow others to be better than Li Xuan. The most he admits is that he is second in mathematics in this class, and third is irrelevant. Not only in algebra and geometry, but also in number theory.

Walking to Li Xuan's desk, Liang Zhihui picked up Jiang Shu's certificate and took a look. Sure enough, he found that it was a fake certificate again. He sneered and said, "Jiang Shu, you are stupid. Don't use this false certificate to embarrass yourself."

"What's wrong?" Jiang Shu stared, unconvinced.

Liang Zhihui sneered: "Let n=2*3*5*7...*p (p is a prime number), then n+1 and n-1 are twin prime numbers? n+1 and n-1 are twins, yes,

But n+1 and n-1 are more likely to be composite numbers, and the probability of being prime numbers is extremely small. Your proof is messy, and you take it for granted."

Jiang Shu picked up his proof and read it again. Suddenly his face turned red. He realized that he had made a logical mistake. The original excitement was completely gone, leaving only embarrassment.

Liang Zhihui said: "Please, please, don't make up for these useless things. Li Xuan's number theory is very strong, definitely much better than mine. If you can prove that he has already proved it, it will be your turn. Not to mention that in history

, there are so many great mathematicians who have failed to solve this conjecture, and now there are so many talented mathematicians in the world who are at a loss. It is impossible for high school students to prove this conjecture."

Li Xuan didn't speak, neither hit nor encouraged. He could only say that Jiang Shu was a little naive. This actually made Li Xuan think about it. The content of the twin prime number conjecture is simple enough for primary school students to understand. What is missing in the proof? Is it true in number theory?

Should we introduce postulates just like Euclidean geometry?

I can't understand.

Jiang Shu was shocked and felt ridiculed. He quietly returned to his seat. He didn't want to go to eat, so he picked up the proof of twin prime numbers and looked at it, frowning.

He found that he couldn't understand, and thought of Goldbach's conjecture again. Is it possible to prove Goldbach's conjecture?

Li Xuan ignored him and left with the others to eat in the cafeteria.
Chapter completed!