Time is not emotional, it passes very slowly when waiting for paychecks, and it passes very quickly when it comes to exams.

Shen Qi didn't make any effective moves in an hour, and there wasn't much time left for him.

Is it over, is it all over.

Is this my limit?

No, this shouldn't be the fate of the top students.

I used to hang up a lot of subjects.

I also used to play games all night.

I used to have the rank of King.

In the blink of an eye, he became a scumbag.

I was lost, disappointed, and lost all directions.

Until you see math, it's the only answer.

Shen Qi thought a lot in this hour, and when he was cranky and recalled the past, it showed that he really had nothing to do.

What is the origin of this array of numbers? It looks like a group, but I've never seen such a strange group, full of magic. It might be a fake group, right? It's not a group at all?

racked his brains to search in the brain knowledge base, and only ...... responded to Shen Qi The knowledge point you are calling is not in the service area.

There is no way to do it, no matter how strong the brain is, if there is a blind spot in knowledge, it will give up treatment.

This is the only way to do this unless you create a completely new set of theories yourself.

But Shen Qi currently does not have this kind of self-contained grandmaster level.

"Maybe I got a full score in the exam every time before, and it was too smooth along the way, how to say that sentence, the sky will descend on the people, and they must first suffer their minds and take away their sisters. ”

Shen Qi in the predicament was cranky, thinking about it and laughing at himself, Lao Tzu is so talented, is this a level 1 language level?

"Teacher Tian, you can't save me this time, the sixty system is useless here. ”

"Director Liu, the algebra knowledge you talked about is too exaggerated, I didn't use it at all this time, I can get to this point by myself. ”

"Teacher Zhang, I haven't seen you for a long time, and when I was in the fourth grade of mathematics, you stopped opening a small stove for me, saying that there was nothing to teach me. ”

The past scenes are played in Shen Qi's mind in a fragmented way, the experience of the past few months is like a dream, if you can get the first place in the IMO world, it will be the most beautiful dream.

"Teacher Zhang, I went to your office a few months ago, and you asked me where I had learned. ”

"I said that I learned about the Gloria transition matrix and the Weierstrath quadratic type, which was a bit of a pretense at the time, and I didn't know much about it at the time. ”

"And then you're instantly confused. ”

"I can't forget this scene, and since then I have started the road of being a top student. ”

"Hehe, time flies so fast, it's the third year of high school in a blink of an eye. ”

"Huh...... it!"

Shen Qi was excited, he suddenly caught a trace of inspiration, fleeting, if it was about to leave.

This feeling is familiar, the finale of the domestic number union national duel at the beginning of this month, it was this kind of over-electric inspiration that saved Shen Qi, Mr. Tian saved Shen Qi, he showed a cuneiform sexagesimal to prove that the root number 2 is an irrational number, and showed the national finale.

"Rewind, rewind. ”

Shen Qi replayed the cranky thoughts just now in his mind.

"Teacher Zhang, I went to your office a few months ago, and you asked me where I had learned. ”

"I said, I learned about the Gloria transition matrix and the Weierstrass quadrat. ”

......

"Although on the surface mathematics is nothing more than a language or a tool, most of its vivid concepts provide the key to new fields of thought. ”

"Determinants and matrices, on the other hand, are completely reforms in the language of mathematics, and Shen Qi must be deeply aware of this in order to make a difference in algebra. ”

......

Shen Qi smiled, very happy, there is no endless road.

Last time, Mr. Tian saved him, and this time Mr. Zhang saved him.

In fact, Shen Qi should be most grateful to himself, he never chose to give up in the predicament, mathematics often requires persistence and even madness, he and his last stubbornness saved him.

The Gloria transition matrix and matrix theory, which were used in the past, finally played a role at the most critical moment.

No matter what kind of demons and monsters this digital array is, whether it is a group or not, it can't escape the demon mirror --- matrix in my Shen Qi's hand.

The tool that can comprehend or translate group theory is the matrix.

Array according to the number of the face:

1=1

196884=196883+1

21493760=21296876+196883+1

864299970=842609326+21296876+2*196883+2*1

......

Shen Qi writes a matrix homomorphism:

A（gi*gj）=A（gi）* A（gj）

Expand it into a matrix representation:

|Ag-0|

|Ai-0|

|0-Aj|

......

This matrix language may seem complex, but the meaning is very simple and straightforward, that is, a matrix representation of a group G, which is a homomorphic mapping of the element g of G to a set of fixed-order nonsingular square arrays A(g).

To put it more simply, swarms are a very difficult set of complex ciphers to understand, and matrices are one of the mothers to decipher the codes.

The only requirement is that you must be proficient in various decoding methods, the more the better.

If you can describe this numerical array with a matrix, it means that it is some kind of group, otherwise it is not.

When Shen Qi expressed this number array in a regular substitution method, he was very surprised: "MMP...... Monster-Group...... It's really a demon and a monster, a demon group!"

What is a swarm?

i.e. the largest scattered monogroup.

Compared to the other groups, the age of the demon group is very young, only about forty years.

This group is quite terrifying, so it was named Monster-Group by mathematicians.

It is difficult for ordinary people to play with the demon group, and when they play, they will go crazy and play badly.

The British mathematician Bocherz made a significant contribution to the theory of the magic swarm, and he proved the "magic swarm moonlight conjecture", an existence that is very magical and awesome just by looking at the name. Bocherz was awarded the Fields Medal for his great achievement.

If you want to play with it, you need at least a PhD in mathematics at the entry level.

Why does this kind of question appear on the IMO exam paper?

Is there a middle school student in the world who can handle it?

Of course not.

You don't need to get it done.

Shen Qi's understanding is that for this demon group, it is OK to give two different forms of mathematical explanations.

Cracking a horde and describing a horde are two different things.

No one can decipher Goldbach's conjecture, but many can describe Goldbach's conjecture: any even number greater than 2 can be written as the sum of two prime numbers.

Similarly, Shen Qi wants to do the latter, but not in words, but in pure mathematical language.

He uses two matrix languages to will

1=1

196884=196883+1

21493760=21296876+196883+1

864299970=842609326+21296876+2*196883+2*1

......

Just express what it is, you don't need to crack it.

This question examines the knowledge and the skillful use of matrices.

We all know that there are many matrix representations of a group, because the order of the matrix can be changed.

"Let's start with the Gloria Transition Matrix. Shen Qi sacrificed Kailai, the founder of the matrix theory, and used the Kailai transition matrix to express the first interpretation of the demon group.

"One more time to the standard matrix. ”

Soon, Shen Qi wrote two different ways of expressing the matrix.

Seeing that there was still time, he came with another shot, and the third shot was the Hermitian matrix.

"If three shots aren't enough, then three more!"

Shen Qi killed the sexuality, click, click, click, and he successively wrote the Klein abstract group matrix, the Weber prime domain matrix, and the Hensel reversible element matrix.

Six shots!

Six shots in just over an hour!

"My body is not hollowed out, if six shots are not enough, then six more shots!"

Shen Qi has never been so cool, a kind of cool crookedness for the rest of his life.

Jingle bells.

That's when the bell rings.

The 4.5-hour competition time has arrived.

"Six shots, only six shots...... It's a pity. Shen Qi didn't have time, he only wrote six matrix languages, and he was a little annoyed.

After handing in the papers, Shen Qi saw the Russian players and the Indian-American players talking and laughing together, and seemed to be full of confidence.

"There are many masters in the world, and I'm not the only one who can do this. "Shen Qi has devoted his life to what he has learned in this IMO, what kind of results can be achieved, let it be fate.

The marking work began in the afternoon of the same day and continued until the early morning of the next day.

The leader of the jury, Professor Wiles, is sixty years old and still insists on his job.

I can't remember how many cups of coffee he refilled, but Professor Wiles was sleepy.

In front of him there were four exam papers, all with a perfect score of 42, from four different countries, Russia, the United States, South Korea, and China.

After a long hesitation, Professor Wiles finally made up his mind, and he graded a "+1" after a perfect score of 42 on one of the papers.

In the last question, the other three perfect scorers all used two methods to give mathematical explanations.

And the player of "42+1" used six types, which is just equal to the sum of the other three players.

The "42+1" player is from China and his name is written in English as Shen-Qi.

The first player with 42+1 points in IMO history was born, his name is Shen Qi.

......

......

This chapter says:

The demons are 541448173