I just want to be a quiet scholar

Chapter 47 This question is so magical

Shen Qi had just finished writing the third algebra problem, and something that made him a little nervous happened.

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

The invigilator walked up to him and put his exam papers in a file bag and sealed it.

The Indian-American contestant walked out of the exam room with ease, looking unstressed.

"Don't be influenced by American Indians, who are mad by others, and the breeze blows the hills."

Shen Qi's attention returned to the test paper, completing the infinite sequence of standard orthogonal elements that he had not yet completed.

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

"He is swayed by him, and the bright moon shines on the river. There is no need to compete with them for speed. What I want is absolute points, not seconds."

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

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

The six members of the Chinese Olympic Math Team immediately returned to the hotel to gather and exchange information. The deputy team leader and various professional coaches acted as military advisors to help them make suggestions.

"How did you feel on the first day of the exam?" the deputy team leader asked the players.

"Disaster."

"It's difficult."

"It's harder than last year."

"It's really a bit difficult. I've done IMO real questions for nearly 5 years. I don't care about the first logic question this year. The analytic geometry and algebra questions that follow 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 of the US team, and the left-handed player of the Russian team."

The deputy team leader took a look at the player's seating chart: "The Indian-American player of the American team is called Arrasin. This year is his second time participating in IMO. Last year, he participated in IMO with full marks and tied for the individual champion. 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 hardware and one silver, none of them scored full marks."

"Indian children are so hung up?" Shen Qi felt that the Indian player who competed with him was not very good-looking, even a bit wretched, and he didn't look like a math genius.

That handsome Russian guy put a lot of pressure on Shen Qi, mainly because the Russian players were so handsome, with blue eyes, a straight nose, and a beautiful blond hair, and she cried. No one is cool and stressful.

The deputy team leader said: "Indians can also be ranked in the world in terms of mathematics level. Shen Qi, you should have heard of the Ramanujan Award, which is one of the awards in the world after the Philippine Award. It is famous for 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 on the field with you is called Peter Bolasdlavsky. Don't be fooled by his appearance. This handsome Russian guy is a recognized math genius. He has participated in IMO for three consecutive years. The first two times got full marks. This Peter has been admitted to the Paris Normal University, one of the top three mathematics majors in the world. Because he has not yet reported to France, he retains 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 for the third consecutive championship. Compared with the United States, which is a multinational force, I am more optimistic about this Russian team. If the other players in Russia play well and cooperate with the ace player Peter , they are very likely to steal the team championship from us." The deputy team leader said, showing a pessimistic look.

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 Non-Euclidean geometry theory, I was born in Ye Luzi and I have not received systematic non-Euclidean geometry teaching, Lobachevsky is my non-Euclidean geometry enlightenment teacher, I respect him very much, although he has passed away for more than 100 years."

"Because of the existence of Peter and Al Racine, 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 our individual level on the premise of ensuring the team championship."

What the deputy team leader said was actually nonsense. The team ranking that calculated the total score was, to put it bluntly, the accumulation of the personal 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 ahead to boost the total score.

Although the Chinese Olympic math team has won three team championships in the past five years, the deputy team leader knows very well that we lack that kind of ace player with outstanding personal strength. Son, what is missing is the king.

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

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

There is a lot of regularity. Players with full marks either don’t get full marks, and once they get full marks, they take them consecutively.

The three most famous contestants in the history of the Chinese Olympiad all conform to this international practice. All three of them have participated in the IMO for two consecutive years and have achieved full marks for two consecutive years. They are known as genius boys.Two of the three talented teenagers were recommended to Yan University and one was recommended 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 tie the world record of "three consecutive games with perfect scores" created by Romanian players.

Shen Qi didn't want to leave regrets for himself. Apart from the team championship, he also wanted to win the No.1 gold medal, which is the individual championship.

Also according to international practice, the Indian players of the US team scored full marks last year, and the handsome Russian left-handed guy won two championships last year and the year before. These two strong enemies are very likely to continue to score full marks this year.

Therefore, in order to become the No.1 individual gold medal in this year's IMO, Shen Qi must ensure a perfect score.

The next day, the second day of the IMO competition.

Before the start of the match, Shen Qi had a face-to-face with Russian player Peter Bolasdowski in the same exam room.

"Hey-man." Shen Qi took the initiative to say hello to Peter Bolasdowski.

Peter-Polasdravsky nodded: "Prupulka is not rude," in Russian.

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

Peter Polaski shook his head and said no.

Oh, it seems that the genius boy in Russia is an English scumbag, not as good as what I said.Shen Qi had nothing to do, and I didn't know Russian, so I couldn't communicate.

The handsome Russian guy stopped paying attention 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 boringly. The two were tied for individual champions last year, and Shen Qi didn't have any record in the international arena, so they didn't take him to play.

If you don't bring it, don't bring it, anyway, I can't have a lower score than you.

Shen Qi adjusted his state and prepared to fight.

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

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

"This last question...seems very perverted. Leave it alone and finish the first two questions."

Shen Qi had to plan his tactics, he had already prepared for the worst, and this last question was probably created by a god, I couldn't even read it.

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

There must be some psychological pressure, but fortunately, the answers to the first two questions went relatively smoothly.

The last question starts with just 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 screen of The Matrix. What is their pattern?
The first thing Shen Qi has to do is to find the law, and then explain the law in mathematical language.

At first glance, it seems a bit regular. There are always numbers in the next row that overlap with the previous row, but the problem is that the sample size is insufficient. Shen Qi can't explain this array of numbers in any mathematical language. It is by no means a Pascal triangular array. of.

Shen Qi pressed his temples vigorously, worried.

Not far away, Russian player Peter Bolasdlavsky and Indian-American player Al Racine didn’t seem worried and were looking through their own reference materials.

Shen Qi also brought three reference materials, he turned the book, but the result was disappointed, and it was useless to turn the book.

In Shen Qi's knowledge reserve, he didn't know which book recorded a similar array of numbers. Wouldn't this thing be the latest research result?
Peter Bolas-Dravsky and Arrasin were flipping through the book while answering, and Shen Qi was even more worried. Maybe the American and Russian syllabus is different from that of China. Did they learn this stuff?
(End of this chapter)