Chapter 11 The sixth question of the IMO legend? !

Regarding this situation, Ding Ping didn't know what to say for a moment.

He always felt a sense of unreality.

Just randomly find a very talented student, and he turns out to be a genius who has a chance to enter the world's top mathematics competition?

Of course, this only means there is a chance. After all, looking at it now, Lin Xiao has only scored 250 points, but there is still 50 points left.

Maybe Lin Xiao just had difficulty with this last question?

But even if the difficulty lies in the last question, at least he can write down some steps. By then, Lin Xiao might be able to get a score of 200 or 300, which would be 270 or 280.

In fact, scoring 200 points already has a high chance of entering the provincial team.

Ding Ping didn't dare to think about it anymore.

The more I think about it, the more outrageous it becomes.

Jincheng City actually produces such awesome students. Generally speaking, such students will be recruited by schools in Xijing during their freshman year of high school.

He didn't doubt whether Lin Xiao had cheated just now, or whether Lin Xiao had done these questions before. He felt there was no need to doubt.

Just based on the first few questions that Lin Xiao answered, there was no need to doubt his personal strength.

Then, he looked at Lin Xiao next to him again, without hesitating his praise at all: "You are very powerful and very talented. You are the most talented student I have ever encountered after teaching in Jincheng Middle School for so long. I believe you are completely You can win the provincial first prize, and you can also participate in the National Mathematical Olympiad. If you then participate in the independent enrollment of some colleges and universities, you will easily be able to enter based on your scores in various subjects and entering the CMO. Going to those famous universities, Qingbei is not a problem.”

"Thank you, Teacher Ding."

It was the first time that a teacher praised her so much, Lin Xiao said shyly.

"Haha, everything I said is true. It's not just to praise you." Ding Ping patted him on the shoulder and said with a smile: "Now I know why you didn't want to come to the training class before, right? Don’t you think there’s any need to come?”

"Uh...a little bit."

"I know you." Ding Ping laughed and shook his head. This kid was also upright and admitted it directly. Of course, he was not angry.

Good students deserve some preferential treatment.

At this moment, the get out of class bell rang outside, and the last period of evening self-study was over.

"Okay, go back. You can take this paper back first. If you have time in the evening, try to write down the remaining questions. There will be a training class tomorrow afternoon. When you come over, show me the paper. ." Ding Ping said: "You still have to come to the training class. There are only four classes per week. The training class classroom is in 303 of the laboratory building. Remember to come."

"Okay." Lin Xiao nodded.

The teacher invited him personally, so of course he was too embarrassed to refuse. Moreover, he could also see that Teacher Ding showed appreciation for him in his words.

You can't let people down. When the time comes when you get the results, Ding Ping will feel bright on his face.

Then, he took the paper and left the office.

He first went back to the classroom to pack his schoolbag, because school was over and most of the day students in the class had gone home, leaving only some boarding students still studying in the classroom.

He didn't stay any longer and went straight back home.

After returning home, of course, it was indispensable to give good news to my mother and father. Father Lin and mother Lin were overjoyed when they learned that their son actually got the first grade in the exam. He paid two hundred yuan and gave it to Lin Xiao as a reward.

After that, Lin Xiao took out the paper again and started writing.

In terms of time, he still has 110 minutes to solve the remaining questions, including the third question, which he has already done half of, and the last question.

In fact, in terms of difficulty, the last two questions of the paper are higher, because among the four questions in the second test, the first two questions are worth 40 points, and the last two questions are worth 50 points.

Each question has a different direction. The four questions are divided into AGNC, namely algebra, geometry, number theory, and combination.

Therefore, in the league, the latter two questions require great attention.

In the paper Lin Xiao is doing now, the first three questions of the second test are algebra, combination, and geometry, and the fourth question is number theory.

Regarding the third geometric proof question, Lin Xiao already had an idea in school. Now that he picked up the pen, he quickly started writing along the original idea.

Of course, it was still difficult, and it became more complicated toward the end, so it took Lin Xiao another ten minutes to finally complete the proof of this question.

He turned around and checked it quickly again. His checking speed was also very fast. After all, the previous ideas were all in his mind. Now he just wanted to see if there were any bugs from the beginning.

Soon, he nodded with satisfaction: "Well... basically there is no problem."

"Then let's start the last question."

The last question is a number theory question.

Number theory is a type of pure mathematics that mainly studies integers, such as prime numbers, such as Goldbach's conjecture, twin prime conjecture, etc. It also studies other issues related to integers.

The difficulty of number theory is also well known. The two conjectures just now are unfamiliar. Even the Riemann Hypothesis, which has stumped mathematicians for more than a hundred years, also belongs to the category of number theory.

Of course, the number theory questions on this paper were obviously not as difficult as those famous conjectures. However, its difficulty still made Lin Xiao frown.

This question is: [Positive integers a and b make a+1 divisible by a+b. Verify: (a+b)/(ab+1) is the square of a certain positive integer. 】

As soon as he got this question, Lin Xiao felt something was wrong. The difficulty was completely different from the previous questions.

The first is the question of where to start. It was easier for him to find where to start with the previous questions, but this question was different. The question stem was very short, but it was difficult because of its short length.

"interesting."

He muttered in his heart, and then fell into thinking.

…

On the other side, Teacher Ding Ping returned to his teacher's dormitory, then picked up the paper he gave Lin Xiao before and started reading it.

No matter what, he would still tutor Lin Xiao tomorrow. If he didn't read anything and just followed the reference answers and taught others, wouldn't that be misleading?

So he also planned to make this paper himself.

Of course, considering that it was relatively late now, he did not do it directly. Instead, he planned to look at these questions first and see if he could come up with ideas.

In this way, after reading for an hour, he saw the last question, and he basically had a vague idea of ​​the previous questions.

As a national-level mathematics teacher, he still has a lot of skills.

"Well, the last question is number theory."

He looked at the question stem and suddenly frowned.

"Hey, where have you seen this question before?"

He immediately looked at the back of the question number. If it was a real question, it would usually indicate where it came from.

Soon he saw that this question came from [1988 IMO Question 6].

He was suddenly stunned. Isn't the sixth question of IMO in 1988 the super difficult question called the "Legendary Question Six"?