How difficult is the sixth question of the IMO legend? In 1988, a total of 268 players from various countries participated in the IMO, but only 11 of them got full marks on this question.
Among these eleven contestants was a future Fields Medal winner, Wu Baozhu.
Among the people who were stumped by this question, there were also some later well-known mathematicians, such as Terence Tao, who got a full score of seven points on other questions, but only got 1 point on this question.
In addition, even the topic committee and four-number theory experts failed to solve this problem within the six-hour limit.
This shows how difficult this question is, and therefore, it was deemed extremely difficult by the topic committee and became the "legendary sixth question" in IMO.
But what makes Ding Ping a little confused is why this question is given here in this simulation paper?
Is this a blow to students’ self-confidence?
Fortunately, he hasn't distributed this paper to the students in the training class yet.
But soon, he thought of Lin Xiao again.
After Lin Xiao went back, he probably had already written out the third question and started working on the fourth question, right?
Can he do it?
Although he had seen Lin Xiao's talent today, Ding Ping did not have high hopes for this famous and even legendary problem.
IMO, such a difficult question is generally not asked. The original question was actually based on a little emotion of the person who asked the question, so such a question was carefully designed to make it difficult for contestants from all over the world.
Moreover, such a difficult question also places great demands on the skill of the questioner.
Ding Ping shook his head and stopped thinking about it. He could only wait until tomorrow's training class to explain it to Lin Xiao, so as not to affect his mentality later.
…
In Lin Xiao's house.
"...According to (1), a2 must be an integer;
According to (2), a2 cannot be 0;
Since a1≥b1, a2 must be less than a1
But since a1 is already the minimum solution of the equation, a2 should not be less than a1, because this is inconsistent with our saying that a1+b1 is the minimum value of the sum of the solutions of the equation, so the two contradict...
So ultimately we can prove that (a+b)/(ab+1) is the square of a positive integer.』
Certification completed.
Lin Xiao couldn't help but wipe his sweat after writing the last two words in a ritualistic stroke.
"I was almost stumped by this question, but luckily I'm better at it."
He breathed a sigh of relief. He was really stumped at first, but fortunately, in the end he came up with a better logic, which was to use proof by contradiction to prove that "there is no minimum, only smaller", and then
Proof of completion.
He was quite impressed with his method of proof.
"As expected of me."
Satisfied, he put down the paper and looked at the time. There was still half an hour, but it took him almost sixty minutes to solve this question, which was far longer than the other questions.
Seeing that it took him so long, Lin Xiao couldn't help but frowned: "It took so long. If this kind of question is asked in official competitions, wouldn't there be no time?"
"Sure enough, I have to study more seriously. Some other math masters may be able to write this question in more than thirty minutes."
"However, it seems that it is meaningful to participate in this training class. Otherwise, I don't know that I would still take such a difficult question."
He completely ignored the question source marked after the question number. After all, he usually did too many questions, so it was normal to ignore this kind of mark.
If he knew that this question actually came from IMO, he probably wouldn't think so much.
However, at this moment, the system sound sounded again.
"The host successfully solved a very difficult problem at the current stage using an extremely brilliant method. The reward is: +6 mathematical experience, 5 hours of sage status, and +1 truth point."
"Tip: The host's math level has been successfully upgraded from level 0 to level 1. The current level is: level 1 (1/50)."
"Sage State: After turning on the Sage State, the host's brain development will be greatly improved."
Lin Xiao was stunned for a moment, what the hell?
The experience is directly increased by 6 points?
How could this question be so recognized by the system?
He was very surprised, because he thought that this question was just an ordinary league math question, but it was a bit difficult. But after he solved it, the system directly rewarded him with six experience points, a little truth point, and even
There are still five hours left...
Uh, sage state?
Although he wanted to complain about this name, after seeing its effect, Lin Xiao forgot about the disadvantages of this name.
This reward is quite awesome!
When the state is turned on, he can actually improve his brain development. This means that if he turns on this sage state when he encounters a problem, he will have a greater chance of solving the problem.
"How much can this sage state improve my brain development?" he asked curiously.
"Depending on what the host body can tolerate, it can increase by 50%."
Lin Xiao thought about it, "With an increase of 50%, my current development level is 2.7%. After it is turned on, it will be equivalent to 1.35%."
This made him look forward to it. Before, he felt a sudden improvement after only increasing it by 0.5%. How strong would it be if it were directly increased by 1.35%?
Einstein, or Newton level?
Of course, maybe the brains of these two big guys are more developed.
He shook his head and stopped thinking about it. He was probably still far behind these two big guys.
At this time, he turned his attention to mathematics after he advanced to the next level.
Although he was upgraded, he didn't seem to feel any changes in himself.
He couldn't help but ask again: "System, what's the use of my math upgrade?"
The system replied: "When each subject reaches level 1, the brain development level increases by 0.05%. The current host brain development level is 2.75%."
Lin Xiao was stunned and was immediately surprised. After upgrading, he could actually improve his brain development. He now knew quite clearly how beneficial it was to increase his brain development.
As for why after this upgrade, he did not feel the same headache and dizziness as before when the 0.5% increase was made, it was probably because the 0.05% increase was too small, so he did not feel the burden.
"If you calculate it this way, if my other five subjects are also upgraded, wouldn't it be equivalent to a total increase of 0.3% in development? Then my brain development will be 3%."
Thinking of this, Lin Xiao couldn't help but feel excited. Compared with the temporary improvement brought by the sage state, this permanent improvement obviously made him more excited.
He quickly asked: "Then when I upgrade a single subject to level 2, will the degree of development be improved even more?"
System: "Please host to upgrade a single subject to level 2 first."
The system did not answer, which made Lin Xiao feel a little helpless. However, thinking that he could become stronger after studying, he became more motivated to study.
So I found the exercise set for the math competition from my school bag, and then took out my pen and scratch paper again.
"Study until 1 o'clock tonight and then go to bed!"
…
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