Chapter 81 Gift
The second question is a game question, but this game requires much more brainpower than ordinary games. It requires you to prove that there are 2010^2010^2010 gold coins in the last box.
It was an interesting question. Wu Tong wrote down the solution process with great interest. He used the main condition to set the operation condition, and used the directional condition to calculate the number of operations... Finally, after a finite number of times, he found that there were no gold coins in other boxes, but in the last sixth box, there were 2010^2010^2010 gold coins.
The third question was another difficult watershed question, a rather deep series problem, which combined the usual IMO question-setting strategies, with geometry, algebra, and number theory all appearing.
Thinking further, Wu Tong wrote down the complex argumentation process of the last question without pausing, and finally wrote "In summary, the conclusion is established." After checking his pen, he raised his hand to hand in the paper, and within an hour, Wu Tong walked out of the examination room.
There was bright natural light outside, and after an hour, the temperature was almost the same as before she entered the examination room.
The IMO competition was a complete success. The secondary preparations for going to college early were also a complete success.
When Wu Tong came out, as they stepped into the final examination room, Professor Cheng and Professor Li, who was finally released from confinement, were sitting by the window, basking in the warm sun and sipping fragrant coffee.
Both of them have similar study abroad experiences and can be considered as the new generation of youth. Their acceptance of coffee is much more tasteful than that of Wu Tong, a country bumpkin who stepped out of the country for the first time!
"Congratulations, Wu Tong, you broke the fastest record for IMO test-taking! Are you confident that you can get full marks?" Professor Li smiled and saluted Wu Tong from a distance, "Come, sit over here. I ordered a small dessert and pistachio yogurt ice cream for you. They have just been served!"
Wu Tong still managed the time so accurately. I knew it would not take more than an hour. Professor Li, who was there to translate the questions, was there, so Wu Tong did not need to write the questions by hand today.
"The score, that depends on the judgement of the organizing committee!" Wu Tong smiled with ease. She could still guarantee the correctness of the result, but the specific score would depend on whether the organizing committee would find fault with it.
"Hahaha... don't worry about that. As long as the process is fine and the result is correct, no matter how they dare to mess around, we in China are not afraid of anyone. Teachers are not pushovers!" Li Yishen was in high spirits and domineering. They, the team leaders, all have the power to mark the papers, and no one can blacken their students' grades for no reason.
Wu Tong’s achievements are all there for us, and the organizing committee believes in them and dares not make too many small moves!
While eating desserts and exchanging ideas, from the initial discussion on the last three questions of IMO to further extended discussions in the fields of geometry, number theory, and algebra, Wu Tong's effortless connection, rigorous logic, powerful and ingenious thinking, and in-depth analysis and solutions to problems made the two professors praise Wu Tong's knowledge reserves.
You know, the two of them can be said to be the backbone of Kyoto University. They have been studying mathematics for more than 20 years. I dare not say that they are excellent in mathematics, but I think their knowledge is solid and worthy of their titles and students.
But when I look again at the underage child Wu Tong who was communicating harmoniously with them, I can't help but feel that the waves behind are pushing the waves in front, and the waves in front die on the beach.
When K=1, for all natural numbers k, there are infinite pairs of prime numbers (p, p+2k).
Staring at the ice cream in front of her, which was dotted with pistachio crumbs and had a very different beauty, Wu Tong suddenly fell into deep thought. The conditions for the twin prime conjecture popped up in her mind. The ice cream in front of her was no longer ordinary ice cream, but a series of wonderful formulas with unique mathematical language.
The right Lambda function?
Viongradov's three prime theorem?
Infinite extension of topology...
Wu Tong suddenly had some enlightenment. She instinctively took out the paper and pen from her backpack and began to deduce on the draft paper... She was immersed in her own world, a series of mathematical formulas condensed under her pen, and her thoughts extended infinitely in her mind, stirring up an endless mathematical storm.
p1, p2, ..., pn, let N = p1 × p2 × ... × pn. If N + 1 is a prime number, then N + 1 must be greater than p1, p2, ..., pn
···5*7*11*13···p*3*5*7*11*11*17`````(p-2)/p····
The wind blew in gently through the window, but at this moment, Li Yishen and Professor Cheng no longer had the leisurely and comfortable mood they had just now.
"This is..." Professor Cheng recalled what he had heard before and looked at Li Yishen in disbelief.
"Haha..." Li Yisheng shrugged and spread his hands. He was very familiar with this state. As you can imagine, we witnessed the child's inspiration burst out again.
Did we discuss anything special just now? Were we in the same dimensional space just now?
How come we are still the same, without any inspiration from the white dove, but the kid opposite us, at this moment, writes eloquently and starts attacking the twin prime conjecture in front of us?
The small round table for resting was not big. Even without moving, the two of them could see what Wu Tong had started to write. The familiar formula appeared, and they both thought of the twin prime conjecture that Wu Tong had been studying.
All I can say is that our brains are really different from those of geniuses. To geniuses, the traces of wind, the outlines of surging white clouds, and even the patterns on ice cream... in their eyes, they are all extensions of mathematics!
The two teachers dared not make any sound at this moment, performing a silent pantomime. Li Yisheng smiled silently, but could not hide the excitement in his eyes. He was worried about his brain, but also excited. Such a child belonged to China and was a student of their Beijing University! He could even shamelessly say that he had taught a student!
Li Yisheng and Professor Cheng were alert and looked after the surrounding environment, preventing anything that might destroy Wu Tong's inspiration and interrupt the inspiration that could give birth to another miracle. They also carefully helped Wu Tong put away and preserve the draft papers she had placed on the table. These would all be treasures of cultural relics in the future!
Wu Tong continued to deduce this until the end of the exam, then she raised her head to stretch her shoulders and neck, and met two pairs of eyes that were looking at her eagerly and passionately.
"Teacher Li, Professor Cheng, what are you doing?" She was almost scared.
"Wu Tong, have you...proven it?" Li Yisheng and Professor Cheng lowered their voices and asked in a low and obscure voice. This is not in China, so it is not too cautious.
Wu Tong shook his head. "It's not even the end yet. How can it be that simple?"
Oh, that's good. Li Yishen and Professor Cheng breathed a sigh of relief. The phased progress was good. Every new step was a gain. They just breathed a sigh of relief and were about to comfort Wu Tong, telling her not to worry, as her breakthrough and progress were already very fast.
Wu Tong paused and then continued, "Fortunately, the general direction has been decided. I should be able to send myself a gift of proof before my birthday!"
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