As a professor in the Department of Mathematics of Peking University, Chen Bing's level is really high.

Starting from the introduction of the topic, it slowly deepened, and at first a few team members listened very easily, and Yue Hao cooperated to say a few stalks from time to time.

But the further back you go, the more pressure you get to understand.

Everyone took out their pen and paper and began to record.

Occasionally, Chen Bing would ask a few simple questions, and everyone would answer them enthusiastically, but the next few problems required more and more time to think.

The foreheads of the six students couldn't help but shed a trace of cold sweat.

This is the legendary chat??

It's better to do a few IMO training questions, okay??

This level of conjecture, even if they are really little mathematicians, is really unbearable!

Finally, under the devastation of two hours.

Chen Bing ended this "friendly chat" with a smile.

Su Mu rubbed his temples, his head was still running at high speed, and the formulas on the paper were already densely memorized.

......

July 14th.

The first IMO exam has officially begun!

Except that the invigilator has become a foreigner and the examination room has become more spacious, Su Mu didn't feel any other particularly big changes.

The question of the test paper that Su Mu is doing now is the Chinese version, which is translated by the deputy team leader He Yijie.

In international competitions, one of the team leaders or deputy team leaders will be exposed to the test questions before the players, but it is strictly forbidden for the team leader and other staff who have been in contact with the test questions to communicate with the students until the end of the test.

In the 90s, it was said that the North Korean team leader left the team leader's residence without permission, and was finally disqualified from the competition.

Of course, none of this has anything to do with Su Mu.

Three questions.

Three exam papers.

Each question is worth 7 points.

He fixed his face slightly, and looked towards today's topic.

The first topic is geometry, which is quite in line with the IMO laws of recent years.

"Let I be the heart of the triangle ABC, and P be the point inside the triangle."

"Satisfies: ∠PBA+∠PCA=∠PBC+∠PCB."

"Proof that AP≥ AI, and that the sufficient and necessary condition for the equal sign to be established is P=I."

This question does not give a graph, but requires the candidate to draw the diagram by himself.

The main examination is the triangle and circle in plane geometry.

Su Mu was a little surprised, it seems that what Chen Bing said is indeed not wrong, the IMO test questions are not as difficult as imagined, but this geometry is slightly simpler than that in the training team.

Directly set ∠A=α, ∠B=β, ∠C=γ, because ∠PBA+∠PCA+∠PBC+∠PCB=β+γ

So we can know that ∠PBA+∠PCB=(β+γ)2

Since the points P and I are located on the same side of the side BC, the points B, C, I, P, and the four points are conspecific, that is, the point P is on the circumscribed circle m of the triangle BCI.

If n is the circumscribed circle of the triangle abc, then the center of m M is the midpoint of the BC arc of n, that is, the intersection of the bisector AI and m of ∠A.

In the triangle APM, there are AP+PM≥AM=AI+IM=AI+PM

The sufficient and necessary condition for the fixed AP≥AI, that is, the equal sign to be established, is that P is located on the line segment AI, that is, P=I.

It only took five minutes before and after, and Su Mu completed the analysis of this question.

Seven points to hand, cost-effective.

He was still thinking about whether he needed to move up to level 11 in mathematics, but when he looked at such a simple problem, he suddenly felt as if he didn't need to waste skill points.

There was a Turkish brother scratching his ears and cheeks next to him, and Su Mu was a little surprised.

Do you have to think about such a simple topic for so long??

This topic should be at the level of a CMO at best, right?

Soon, Su Mu put this test paper at the bottom and took out the test paper for the second question.

The second question is a little longer.

The investigation is about the segmentation of regular polygons.

"It's a very simple question."

Su Mu read it twice, the description of this question is indeed very long, but the process of solving it is more concise.

"It's called IMO ???"

Su Mu bit the tip of the pen and was very embarrassed.

He would rather have a difficult topic, he is easy to play.

But the topic is so simple, he can't get started.

He's got skill points, but it's useless!

He still has the skill of extreme arithmetic that he hasn't used!

He's ready to show off his skills and go back to the hotel to get some sleep!!

But looking at this situation now, there is no need for Su Mu to play extraordinarily at all.

It is said that the difficulty of today's question is E, C, A, but this E and this C are too simple, if IMO is only at this level, it stands to reason that it should not be a big problem to get a full score!!

Belch.

It seems that the probability of the Chinese team scoring a perfect score in the Olympiad is indeed quite high.

Su Mu suddenly thought of this, and was slightly relieved.

No wonder Chen Bing's eyes have always been very stable when he looks at him, his focus is on several other teammates, and he probably knows that he is a gold medal nine out of ten after looking at the team leader.

sighed.

It's a shame that he's been excited for so long.

These questions are not as difficult as the question of "what gift to bring back to Yan Xiaoke".

Finally.

Su Mu flipped through the test paper and put it on the third one with a little expectation.

This is an A-level question, and according to convention, it should be the most difficult question in this IMO.

"it."

As soon as he saw the title, Su Mu exclaimed.

It's not because this problem is too difficult, or because it's too easy, but because this problem actually relies on Euler's product formula!!

"This Nima... Is it really a millennium problem?? ”

Su Mu's pupils contracted.

Euler's product formula, which refers to the Dirichlet series that can be expressed as an infinite product with an index of primes, proves that the Riemann function can be expressed as a form of this infinite product.

Although it is not a variant of Riemann's conjecture, it was really said by Chen Bing yesterday!!

Yesterday, Chen Bing mainly chatted with them, and the dawn conjecture and M theory were fused, but I didn't expect that in today's competition, I directly tested the Euler product formula!!

This question examines Euler's product formula and the underlying sequence.

A general exceptional outcome needs to be demonstrated.

The proof of Euler's product formula is very simple, and the only thing to be careful about is the treatment of infinite series and infinite products, and the properties of finite series and finite products cannot be arbitrarily used.

Although it is said that the difficulty of the finale question as IMO is enough.

But how Su Mu thought about it and felt a little fantastical.

Could it be that Chen Bing knew the topic in advance yesterday? Came out to chat with them?

However, when Su Mu looked down next, he knew that it was just a coincidence.

Because this proof question is still quite difficult.

It's not just about sequences, it's about the mean theorem.

Chen Bing just mentioned a mouthful of dawn conjecture.

Today's question still depends on the real strength of each player!!

......