I Just Want to Be a Quiet Top Student

The third question, the algebra question, Shen Qi had just finished halfway through, when something happened that made him a little nervous.

The Indian-American contestant stood up and made a hand gesture.

The invigilator walked up to him, put his examination paper into the file bag and sealed it.

The Indian-American contestant walked away from the exam with ease, looking unstressed.

"Don't be influenced by Indian-Americans, let him be crazy, let the wind blow the hills."

Shen Qi's attention returned to the examination paper, and he completed the infinite sequence of orthonormal elements that he had not yet completed.

A few minutes later, the very handsome Russian player handed in the paper.

"He let him go, and the moon shines on the river. There is no need to compete with them for speed. What I want is absolute scores, not seconds."

Shen Qi finally completed the proof, he was not in a hurry to hand in the paper, but checked and checked again, and waited for 4.5 hours before handing in the paper.

The first day of the IMO competition is over, and all contestants' test papers are sealed, and they can only be opened at this time tomorrow.

The six members of the Chinese Mathematical Olympiad team returned to the hotel to gather and exchange information. The deputy team leader and professional coaches acted as military advisers to help them make suggestions.

"How does it feel to compete on the first day?" the deputy team leader asked the team members.

"Disaster."

"Very difficult."

"Harder than last year."

"It's really a bit difficult. I've done real IMO questions for nearly 5 years. Leaving aside the first logic question this year, the following analytic geometry and algebra questions are the most difficult in the past 5 years." Shen Qi explained truthfully, and then added: " And I found that individual players from some countries have good individual combat ability, such as the Indian player on the US team and the left-handed player on the Russian team."

The deputy team leader found out the player's seating table and took a look: "The Indian player of the US team is called Al Rahim. This year is his second time participating in the IMO. Last year he participated in the IMO and got full marks and tied for the individual championship. Yes, that's right, I remember This Indian kid was also the team I led last year. Our Chinese team narrowly beat the US team by 2 points to win the team championship. Although six players won five gold medals and one silver medal, none of them got full marks."

"The Indian kid is so hanging?" Shen Qi felt that the Indian player who was competing with him was ugly, even a little wretched, and he didn't look like a math genius.

That handsome Russian guy made Shen Qi feel a lot of pressure, mainly because the Russian player is so handsome, with blue eyes, a straight nose, and soft blond hair. No one is cool and stressful.

The deputy team leader said: "The mathematics level of Indians is also ranked first in the world. Shen Qi, you should have heard of the Ramanujan Award. It is one of the awards in the world after the Philippine Award. Indian mathematicians named after Ramanujan."

Shen Qi nodded: "I've heard it. Ramanujan is very powerful. Ramanujan's conjecture series is a relatively high-end operation, and I haven't mastered it all."

"Shen Qi, the Russian player with you is Peter Polasdravsky. Don't be fooled by his appearance. This handsome Russian guy is a recognized math genius. He has participated in the IMO for three consecutive years. He got full marks in the first two times. This Peter has been admitted to the Ecole Normale Supérieure de Paris, one of the top three mathematics majors in the world, and because he has not yet reported to France, he still has the qualification to participate in this year’s IMO.”

"There is no doubt that Peter, who participated in the IMO for the last time, is aiming to achieve three consecutive personal championships. Compared with the multinational team of the United States, I am actually more optimistic about this Russian team. , They are very likely to snatch the team championship from us." The deputy team leader said, showing a pessimistic expression.

Shen Qi's expression is also solemn: "Russians are good at mathematics. The only Poincaré conjecture that has been solved among the seven millennium problems was completed by Russian mathematician Perelman. In fact, I often use Lobachevsky's The theory of non-Euclidean geometry, I was born in Yeluzi, and I have not received systematic non-Euclidean geometry teaching, Lobachevsky is my first teacher of non-Euclidean geometry, I respect him very much, although he has passed away for more than 100 years."

"Because of the existence of Peter and Al Razin, it is not easy for any of you to win the individual championship." The deputy team leader said to the six players, "So we must unite and give full play to the individual level on the premise of ensuring the team championship."

What the deputy team leader said was actually nonsense. To put it bluntly, the team ranking calculated by the total score is the accumulation of the individual strengths of the six players. The premise of ensuring the team championship is that there are no shortcomings in the team, and there are one or two ace players charging forward to increase the total score.

Although the Chinese Mathematical Olympiad team has won three team championships in the past five years, the deputy team leader knows very well that we lack the kind of ace players with outstanding personal strength. Yes, we have four 2s plus a small king plus a straight Son, what is missing is the king.

Back in the hotel room, Shen Qi checked the data online.

The data told him that it is not easy to get a full score in the IMO arena, and the number of players with a full score in an IMO is basically in single digits.

It is very regular, the full score contestants either don't get the full score, and once they get the full score, they get it consecutively.

The three most famous players in the history of Chinese Mathematical Olympiad competitions all conform to this international practice. All three of them participated in the IMO for two consecutive years and got full marks for two consecutive years. They are known as genius boys. Two of the three gifted youths were recommended to Yanda University and one to Zhejiang University.

When Shen Qi graduates from high school next year, he will be able to participate in two IMO sessions at most, and it is impossible to equal the world record of "three consecutive perfect scores" created by a Romanian player.

Shen Qi didn't want to leave regrets for himself. Apart from the team championship, he also wanted to win the first place in the gold medal, that is, the individual championship.

Also in accordance with international practice, the Indian players of the US team got full marks last year, and the handsome Russian left-handed guy won two championships last year and the year before last. These two strong opponents are very likely to continue to get full marks this year.

Therefore, in order to become the number one individual gold medalist in this year's IMO, Shen Qi must ensure a full score.

The next day, IMO competed for the second day.

Before the start of the competition, Shen Qi had a face-to-face meeting with Russian player Peter Polasdravsky in the same examination room.

"Hey-man." Shen Qi took the initiative to greet Peter Polasdravsky.

Peter Polasdravsky nodded: "Prupulukaburu." It was in Russian.

Shen Qi asked: "Can-you-speak-English?"

Peter Polasdravski shook his head, saying no.

Oh, it seems that the Russian prodigy is a scumbag of English, not as good as me. Shen Qi was at a loss, and I didn't know Russian, so I couldn't communicate.

The handsome Russian guy stopped talking to Shen Qi. He moved a few steps and hugged the Indian-American player. The two communicated in French and looked familiar.

Shen Qi walked away bored, the two were last year's joint individual champions, and Shen Qi didn't have any record in the international arena, so they didn't take him to play.

If you don’t take it, don’t take it, anyway, I can’t score lower than your test scores.

Shen Qi adjusted his state and prepared to fight.

At 9:00, the competition on the second day of IMO starts on time, and each contestant will face the remaining three questions.

After Shen Qi got the exam papers, he quickly browsed through the three exam questions.

"The last question...seems very perverted. Let's ignore it, and let's talk about the first two questions."

Shen Qi has to arrange a good tactical play, he has already prepared for the worst, the last question is probably made by a god, I can't even understand it.

He didn't dare to expect full marks, Shen Qi was caught off guard by the complicated international situation.

There must be some psychological pressure. Fortunately, the answers to the first two questions were relatively smooth. After two hours, Shen Qi had to face the question of town house in this IMO.

The last question starts with only a bunch of numbers:

1=1

196884=196883+1

21493760=21296876+196883+1

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

...

According to the above rules, please give two different mathematical explanations. (7 points)

This pile of numbers is similar to the opening scene of The Matrix. What are their rules?

Shen Qi's first thing to do is to find the law, and then explain this law with mathematical language.

At first glance, it looks a bit regular. There are always numbers in the next line that overlap with the previous line, but the problem is that the sample size is insufficient. Shen Qi can’t explain this number array in any mathematical language. It is definitely not a Pascal’s triangle matrix. It has an equal sign of.

Shen Qi pressed his temples vigorously, feeling worried.

Not far away, the Russian player Peter Polasdravsky and the Indian-American player Al Rahim, they didn't seem worried, and they were looking through the reference materials they brought.

Shen Qi also brought three reference materials. He flipped through the books, but was disappointed in the result, flipping through the books was useless.

In Shen Qi's knowledge reserve, he doesn't know which book records a similar number array. This thing can't be the latest research result, right?

Peter Polasdravsky and Al Razin answered the papers while flipping through the books, Shen Qi was even more worried. Maybe the syllabus of the United States and Russia is different from that of China. They have learned this stuff before?