From Almighty Scholar to Chief Scientist

Chapter 11 IMO Legend Sixth Question? !

For this situation, Ding Ping didn't know what to say for a while.

He always felt a sense of unreality.

Just randomly find a student with a good talent, who is actually a genius who has the chance to enter the world's top math competition?
Of course, this only means that there is a chance. After all, from the current point of view, Lin Xiao only got 250 points, so there are still 50 points left.

Maybe Lin Xiao happened to be struggling with this last question?
But even if the last question is difficult, at least he can write some steps. By then, Lin Xiao might get twenty or thirty points. That would be two hundred and seventy, two hundred and eighty.

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

Ding Ping didn't dare to think about it.

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

Jincheng actually had such an awesome student. Generally speaking, this kind of student would be recruited by those schools in Xijing in the first year of high school.

He didn't doubt whether Lin Xiao cheated just now, or whether Lin Xiao had done these questions before, he didn't think there was any need to doubt.

Based on the first few questions Lin Xiao did, there was no need to doubt his personal strength.

Afterwards, he looked at Lin Xiao next to him again, and did not hesitate at all for his admiration: "You are very powerful and talented. You are the most talented student I have ever met while teaching in Jincheng Middle School. I believe you are completely You can go to win the first prize in the province, and you can also participate in the National Mathematical Olympiad at that time. If you then participate in the independent enrollment of some colleges and universities, with your grades in various subjects and the fact that you have entered the CMO, you can easily enter Going to those famous colleges and universities, Qingbei is not a problem."

"Thank you, Teacher Ding."

It was the first time that she was praised so strongly by the teacher, Lin Xiao said shyly.

"Hehe, what I said is true, not just to praise you." Ding Ping patted him on the shoulder and said with a smile: "I now understand why you didn't want to come to the training class before, don't you?" Don't you think it's necessary to come?"

"Uh...a little bit."

"I knew about you." Ding Ping shook his head with a grin. This kid was also straightforward, and he admitted it directly. Of course, he was not angry.

A good student deserves some preferential treatment.

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

"Okay, you go back, take this paper back first, if you have time in the evening, try to write the rest of the questions, there will be a training class tomorrow afternoon, when you come over, show me the paper Ding Ping said: "The training class is still coming, and there are only four classes every week. The training class classroom is in the laboratory building 303, remember to come."

"Okay." Lin Xiao nodded.

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

Can't let people down, when the time comes when he gets the grades, Ding Ping will also feel proud.

Afterwards, 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, only some boarding students were still studying in the classroom.

He didn't stop much, and went straight home.

When I got home, of course, I would like to say good news to my mother and father. Lin's father, Lin's mother, was overjoyed when she learned that her son was the first in the grade. She praised her son well. He paid 200 yuan and gave it to Lin Xiao.

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

Calculated according to the time, he still has 110 minutes to solve the remaining questions, including the third question and the last question that he has already done half of.

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.

The direction of each question is different. The four questions are divided into AGNC, that is, algebra, geometry, number theory, and combination.

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

In the paper that 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 geometry proof question of the third question, Lin Xiao already had an idea in school, and now after picking up the pen, he quickly wrote down the original idea.

Of course, there is still some difficulty, and it gets more and more complicated towards the end, so it took Lin Xiao another ten minutes, and he finally completed the proof of this question.

Looking back, he quickly checked again, and his checking speed was also very fast. After all, the previous thoughts were all in his mind, and now he just checked from the beginning to see if there were any bugs or anything.

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

"Then let's start with the last question."

The last question, a number theory question.

Number theory is a kind of pure mathematics. It mainly studies integers, such as prime numbers, such as Goldbach's conjecture, twin prime number conjecture, etc., and 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 conjecture, which has baffled mathematicians for more than 100 years, also belongs to the category of number theory.

Of course, the difficulty of the number theory questions on this paper is obviously impossible to compare with those famous conjectures, but its difficulty still made Lin Xiao frown.

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

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

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

"interesting."

He muttered in his heart for a while, and then he fell into thinking.

……

On the other side, Teacher Ding Ping returned to his teacher's dormitory, and then picked up the paper that Lin Xiao had given to him before and read it.

No matter what, he still has to tutor Lin Xiao tomorrow. If he didn't read it at all and taught others according to the reference answers, wouldn't that be a mistake?
So he also planned to do this paper himself.

Of course, considering that it was relatively late now, he didn't do it directly, but planned to look at these questions first to see if he could come up with an idea.

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

As a national special mathematics teacher, he still has a few brushes.

"Well, the last question is number theory."

He looked at the stem of the question, and suddenly frowned.

"Hey, where did you see this question?"

He immediately looked behind the number of the question. 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 Six].

He was stunned for a moment. Isn't the sixth question of IMO in 1988 the super difficult problem called "legendary sixth question"?
(End of this chapter)