From Almighty Scholar to Chief Scientist

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.

这道题为：【正整数a与b使得ab＋1整除a^2＋b^2，求证：（a^2＋b^2）/（ab＋1）是某个正整数的平方。】

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"?

Chapter 12 Unexpected System Rewards

How difficult is the sixth question of the IMO legend? In 1988, there were a total of 268 contestants from various countries participating in the IMO, but only 11 contestants got full marks on this question.

Among the eleven contestants was a later Fields Medal winner, Wu Baozhu.

Among the people who were stumped by this question, there were also some later well-known mathematicians, such as Tao Zhexuan, who got a full score of 1 on other questions, but only got [-] point on this question.

In addition, even the topic committee and the four number theory experts failed to solve this problem within the six-hour time limit.

It can be seen how difficult this question is, and therefore, it was deemed extremely difficult by the agenda committee and became the "Legendary Sixth Question" in IMO.

But what Ding Ping couldn't figure out was why this question was given here for 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 the third question, and started to work on the fourth question, right?

Can he do it?

Although he had seen Lin Xiao's talent today, Ding Ping did not have much hope for this famous and even legendary problem.

IMO generally does not ask such a difficult question. The question was originally created because of a little emotion of the person who made 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 has great requirements on the level of the question maker.

Ding Ping shook his head, no longer thinking about it, he could only wait for tomorrow's training class to explain to Lin Xiao, so as not to affect his mentality in time.

……

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 contradictory to our statement that a1+b1 is the minimum value of the sum of the solutions of the equation...

So finally we can prove that (a^2+b^2)/(ab+1) is the square of some positive integer. 』

Certificate completed.

Lin Xiao couldn't help wiping off his sweat after writing the last two words with a stroke of ceremony.

"I was almost stumped by this question, but luckily I have a better skill."

With a sigh of relief, he was really stumped at the beginning, but fortunately, at the end he came up with a better logic, which is to use the method of proof by contradiction to prove that "there is no smallest, only smaller", and then it is considered Proof of completion.

He was quite impressed by his proof method.

"As expected of me."

Satisfied, he put down the paper and looked at the time. There was still half an hour left, but it took him more than 60 minutes to solve this question, far exceeding 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 taken in the official competition, 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 30 minutes."

"However, it seems that it is still meaningful to participate in this training class. Otherwise, I don't even know that such a difficult question will be taken."

He completely ignored the source of the question marked after the question number of this question. After all, he usually does too many questions, so it is normal to ignore this mark.

If he knew that this question actually came from IMO, he probably wouldn't think so much.

However, at this moment, the sound of the system sounded again.

"The host successfully used an extremely brilliant method to solve a very difficult problem at the current stage. Rewards: Mathematical experience +6, sage status for 5 hours, truth point +1."

“提示：宿主的数学等级成功从0级升为1级，当前为：1级（1/50）。”

"Sage state: After turning on the sage state, the host's brain development level will be greatly improved."

Lin Xiao was taken aback for a moment, what the hell?

Experience directly added 6 points?

How could this question be so recognized by the system?

He was very surprised, because he thought this problem was just an ordinary league math problem, 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 Five hours to go...

Uh, sage status?

Although I wanted to complain about the name, but after seeing its effect, Lin Xiao forgot the point of the name.

This reward is a bit powerful!

When the state is turned on, he can actually improve his brain development level, which means that if he turns on the sage state when he encounters a problem, he will have a greater chance to solve the problem.

"How much can this sage state improve my brain development?" He asked curiously.

"Depending on what the host body can accept, it can increase by 50%."

Lin Xiao thought about it, "The increase is 50%, and my current development level is 2.7%, which is equivalent to 1.35% after opening."

This made him look forward to it. Before, he felt a rapid improvement just by increasing it by 0.5%. If it was directly increased by 1.35%, how strong would it be?

Einstein, or Newtonian?

Of course, maybe these two bigwigs have a higher degree of brain development.

He shook his head and didn't think about it anymore. He was probably still far away from these two big men.

At this time, he turned his attention to the mathematics after he was promoted to the next level.

Although he had upgraded, he didn't seem to feel any change in himself.

He couldn't help asking again: "System, what's the use of my math after upgrading?"

The system replied: "When each subject is upgraded to level 1, the brain development degree increases by 0.05%, and the current host's brain development degree is 2.75%."

Lin Xiao was stunned for a moment, and was immediately pleasantly surprised that the degree of brain development could be improved after the upgrade. Now he is quite aware of the benefits of increasing the degree of brain development.

As for why after this upgrade, he didn't feel the headache and dizziness he felt when he had increased by 0.5%, it was probably because the increase of 0.05% was too small, so he didn't feel the burden.

"In 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 reach 3%."

Thinking of this, Lin Xiao couldn't help but feel excited. Compared with the temporary improvement brought about by the status of a sage, this permanent improvement obviously made him more excited.

He quickly asked again: "Then when I upgrade to level 2 in a single subject, will my improvement be higher?"

System: "Please ask the host to upgrade a single subject to level 2 first."

The system didn't answer, which made Lin Xiao feel a little helpless. However, thinking that he could make himself stronger after studying, his motivation for learning was even more sufficient.

So I found the problem set of the math competition from my schoolbag, and then took out the pen and draft paper again.

"Sleep until 1 o'clock tonight!"

Chapter 13 Ding Ping's Surprise

On Monday, the senior three classes continued as usual.

Lin Xiao, as No.1 in the grade this time, also enjoyed the treatment of a top student. Even the female students sitting in the back seat came to ask him math problems.

And his appearance is also a little handsome, that is to say, the students in their rocket class are all good students, and they are all focused on their studies. If they go to ordinary classes, maybe there will be a few girls in the class chase him.

In this way, in the sound of "Lin Xueba", he gradually lost himself... Ahem, this is of course impossible, he just thinks more and more that learning is really the most important thing.

So, he studied hard for another day, and he didn't stop until the afternoon when the mathematics competition training class started.

Then, he took last night's league papers, along with paper, pens and teaching materials, and headed to the training class.

Jiang Jie was also going, so he happened to be on the same path as Jiang Jie.

Jiang Jie looked at Lin Xiao who walked to the laboratory building with him, and asked suspiciously: "Lin Xiao, are you coming to the laboratory building too?"

Lin Xiao nodded, "That's right, Teacher Ding Ping asked me to come to the mathematics competition training class, so I came here."

Jiang Jie was taken aback for a moment, showing a look of "I heard you right", and said, "Mr. Ding, did you come to attend the training class?"

"Yes."

Seeing Lin Xiao nodding, Jiang Jie was even more confused: "What about Xu Lin? He didn't come?"

"Why don't he come? Teacher Ding only called me here alone. I was at Teacher Ding's place last night. He tutored me and then asked me to come to the training class."

Jiang Jie was even more puzzled. Teacher Ding actually tutored Lin Xiao alone?