I Just Want to Be a Quiet Top Student

　　 The third question of algebra, Shen Qi just finished writing a half, something that made him a little nervous happened.

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

　　 The invigilator walked up to him, put his test papers in the file bag and sealed it.

　　The Indian-American players left the examination room with ease, seemingly stress-free.

　　 "Don't be influenced by the American Indians, he is crazy by him, and the breeze is blowing on the hills and hills."

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

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

　　 "He is going by him, and the moon is shining on the river. There is no need to fight for speed with them. I want absolute scores, not seconds."

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

　　 The first day of the IMO competition is over, and the test papers of all contestants will be sealed, and they will not be unsealed until this time tomorrow.

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

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

"difficult."

　　 "It's difficult."

　　 "It's harder than last year."

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

The deputy team leader took a look at the table of players: "The Indian player of the American team is called Al Racine. This is his second IMO participation. Last year, he participated in the IMO and got full marks and tied for the individual championship. Yes, yes, I remember. This Indian kid was also a team led by me last year. Our Chinese team narrowly defeated the US team by 2 points to win the team championship. Although six players won hardware and silver, 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 unsightly and even a little wretched. He didn't look like a mathematical genius.

That handsome Russian boy made Shen Qi feel a lot of pressure, mainly because the Russian players are so handsome, with blue eyes, a straight nose, and a soft blond hair, crying. Shen Qi thinks that his looks are inferior to others, and his hairstyle is also good. Nobody is cool and stressful.

The deputy team leader said: "Indians are ranked top in mathematics in the world. Shen Qi, you should have heard of the Ramanu Gold Award. It is one of the world's second only to the Philippine Award. Named after Ramanujan."

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

"Shen Qi, the Russian player with you is called Peter Bolasdravsky. Don't be fooled by his appearance. This handsome Russian boy is a recognized mathematics genius. He participated in the IMO for three consecutive years. He scored full marks in the first two times. This Peter has been admitted to the Paris Normal University, one of the top three majors in mathematics in the world. Because he has not yet reported to France, he retains the qualifications 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 hit his three consecutive championships with perfect scores. Compared with the United States, I am more optimistic about this Russian team. If the other Russian players perform well, cooperate with the ace Peter Peter. , They are very likely to steal the team championship from us.” The deputy team leader said, showing a look of not optimistic.

Shen Qi's expression is also solemn: "Russians are very good at mathematics, and the only Poincaré conjecture that has been solved in seven thousand-year problems was completed by Russian mathematician Perelman. In fact, I often use Lobachevsky’s Non-Euclidean geometry theory. I was born in Yeluzi and I have not received systematic non-Euclidean geometry teaching. Lobachevsky is my 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 Racine, it is not easy for any of you to win an individual championship." The deputy team leader said to the six players, "So we must unite to ensure that the team is champion, and give full play to the individual level."

　　 What the deputy team leader said is actually nonsense. The team ranking for calculating the total score is simply the accumulation of the personal strength of the six players. The premise to ensure a 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 Olympic Mathematical 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 2 plus a king and a smooth hand. Son, what is missing is the king.

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

　　The data tells him that it is not easy to get a full score in the IMO competition. The number of full score players in an IMO is basically single digits.

　　 is very regular, the full score players either do not get full marks, once they get full marks, they will take them in succession.

　　 The three most famous athletes in the history of the Chinese Olympiad are all in line with this international practice. All three of them have participated in the IMO for two consecutive years and scored full marks for two consecutive years. They are known as genius teenagers. Two of the three talented teenagers were recommended to Peking University and one to Zhejiang University.

　　 Shen Qi graduates from high school next year, he will be able to participate in at most two IMO, it is impossible to tie the world record of "full score three consecutive" created by Romanian players.

　　 Shen Qi doesn't want to leave regrets for himself. In addition to the team championship, he also wants to get the first gold medal, that is, the individual championship.

　　 It is also in accordance with international practice. The Indian players of the US team scored full marks last year. The handsome Russian left-handed guy won two championships last year and the year before. These two powerful rivals are likely to continue to score full marks this year.

　　 Therefore, to become the first individual gold medal in this IMO, Shen Qi must ensure full marks.

　　 The next day, the second day of IMO competition.

　　 Before the game started, Shen Qi had a face-to-face meeting with the Russian player Peter Bolasdravsky in the same examination room.

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

　　 Peter Bolasdravsky nodded, "Proplukabulu." He spoke Russian.

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

　　 Peter Polasdravsky shook his head and said he would not.

　　 Oh, it seems that the Russian genius boy is a scumbag in English, not as good as I said. Shen Qi is gone, and I don't understand Russian, so I can't communicate.

　　 The handsome Russian guy stopped paying attention to Shen Qi. He moved a few steps and hugged with the Indian-American player. The two communicated in French, and they looked quite familiar.

　　 Shen Qi walked away boringly. This handsome frustration and the two were tied for the individual champions last year, and Shen Qi did not have any record in the international arena, and they did not play with him.

　　 If you don't bring it, don't bring it. Anyway, I can't get lower than your score.

　　 Shen Qi adjusted his state and prepared for the challenge.

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

　　 After getting the test paper, Shen Qi first glanced over the three test questions quickly.

　　 "The last question...seems to be abnormal. Leave it alone and finish the first two questions."

　　 Shen Qi must arrange his tactical play. He has already planned for the worst. In the end, this question may have come from a god, and I can't even read it.

　　 I dare not expect full marks~www.readwn.com~ The complicated international situation caught Shen Qi off guard.

　　 There must be psychological pressure. Fortunately, the answers to the first two questions went smoothly. Two hours later, Shen Qi had to face the question of town house in this IMO.

　　 The last question opened 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)

　　 These numbers are similar to the opening scenes of The Matrix. What are their laws?

　　 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 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 not enough. Shen Qi can't explain this number array in any mathematical language. It is definitely not a Pascal triangle, it has an equal sign. of.

　　 Shen Qi pressed his temple vigorously, sad.

　　 Not far away, Russian player Peter Bolasdravsky, and Indian-American player Al Racine, they didn't seem to worry, they were looking through their own reference materials.

　　 Shen Qi also brought three reference materials. He turned the book, but the result was disappointed, and the book was useless.

　　 In Shen Qi's knowledge reserve, he doesn't know which book records a similar array of numbers. Isn't this the latest research result?

　　 Peter Bolasdravsky and Alracine answered the paper while flipping the book. 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?