Qiao Yu stood outside the building as usual, watching Principal Zhang and Teacher Lan out of his sight before turning to go home.

For him, doing so not only shows respect for the guests, but also costs almost nothing.

Qiao Yu's purpose is to leave a good impression on useful people rather than leave a bad impression. Of course it's nice to show your personality, but if it conflicts with the potential benefits, then don't let it go for the time being. It will only become the eyes of passers-by. The most beautiful boy can only satisfy his vain vanity.

No matter how nice a passerby's words are, they can't change his life. But the money that goes into his pocket is real good stuff. The merchant will most likely not discount the customer because of his personality, but it may break his bones because the customer is too individual. .

Qiao Yu has always felt that the biggest advantage of a country with a long history is that the ancients have almost summarized all kinds of life experiences. For example, if a gun kills a bird, the wind will destroy it. In short, personality must be the same as ability. Show it when it's time to show it, hide it when it's time to hide it.

Qiao Yu just turned around and walked into the building, and happened to meet Xia Hongliang walking downstairs carrying a garbage bag.

"Uncle Xia." Qiao Yu took the initiative to call out, giving Xia Keke face, and planned to run away and go home.

It was a good idea, but he was stopped by an adult: "Qiao Yu, did you just see Principal Zhang off?"

"Yeah." After saying that, Qiao Yu wanted to leave again, but was stopped again: "Wait a minute, I took out the trash, let's have a chat. I won't waste your time." Qiao Yu thought for a while, but still stood. Waiting at the gate.

The trash can for each unit is not far outside the building. Indeed, Lao Xia walked back directly without waiting for long, then skillfully took out a pack of cigarettes from his pocket, took out one and put it in his mouth. I was about to put it back in my pocket, but then I thought of something, took out the cigarette again, knocked out half of it, and handed it over.

"Do you want it?"

Qiao Yu waved his hand and refused: "No."

"Don't pretend, I saw you had it." Lao Xia glanced at Qiao Yu and said.

Qiao Yu shook his head and said, "I'm not pretending. I did smoke before and quit last month." "Oh? Don't say it was Keke who asked you to quit." Lao Xia couldn't help but tease.

Qiao Yu shook his head again and said, "No, it's that Teacher Lan. He said that if I want to participate in IMO, I have to quit smoking. Otherwise, he won't take me to play." Lao Xia was a little bored. .

It's not that Qiao Yu chose to quit smoking because of his daughter, but because he didn't quite understand what IMO was and was too embarrassed to ask. He just felt that young people nowadays are impetuous and have too many new words.

Fortunately, Qiao Yu probably saw something and took the initiative to explain: "IMO is the abbreviation of International Mathematical Olympiad. There is no way, people who use Indo-European languages ​​like to make abbreviations to make people listen. "In the fog."

Lao Xia was stunned for a moment, silently put the cigarette back into his pocket, took out a lighter and lit it for himself, took two strong puffs, and then laughed at himself: "You are a ruthless person, you can quit if you say you want to, but I am like this I'm afraid I won't be able to quit for the rest of my life, because I still get scolded by your Aunt Liu every day." Qiao Yu smiled and flattered: "That's because Uncle Xia, you often have to work the night shift and you just need to refresh yourself. I really want to transfer you to work every day. Just stay on the train and you can quit. People's habits are all passed down."

Lao Xia smiled. This boy was still as smart as before and always spoke so nicely.

"Come on, you also know that Uncle Xia and I are a serious roughneck, and my grades are not good since I was a child. I was able to join the railways back then because I was in the same position as my father. I will probably be like this in my life, and I won't have much future." .

Unfortunately, this poor job is long and time-consuming, and I have to follow the car for several days. I am just such a girl, and I can’t take care of it. Fortunately, Keke is still up to date. In fact, I have to thank you. If it weren’t for you, Keke This kid probably isn’t that confident yet.”

Qiao Yu smiled politely. It was not easy for him to accept these words, especially when he could not judge the intentions of this middle-aged man.

"Now this girl doesn't even listen to what her mother and I say, she just listens to you. I'm not saying it's not good, but this girl has a bit of an awkward temperament. It's really annoying to follow her mother sometimes. If she does it in the future I've annoyed you so much, give Uncle Xia some face and don't let her get off the stage."

Lao Xia said humbly.

Qiao Yu immediately said: "Don't worry, Uncle Xia, Keke has been playing with me since she was a child. I have always regarded her as a younger sister, and I will definitely take care of her as a younger sister in the future."

A smile finally appeared on the weathered face of Lao Xia, a middle-aged man. He took a last puff, flicked the cigarette butt away without any quality, then reached out and patted Qiao Yu on the shoulder: "With you, That’s all, let’s go home.”

After returning home, Qiao Yu was looked up and down strangely by Qiao Xi.

"What's wrong?" Qiao Yu asked inexplicably.

"Why do you have to stay outside for so long every time you send that good old man off?" Qiao Xi asked curiously.

"When I came back, I met Uncle Xia going downstairs to throw away the trash, so he pulled me to chat for a few words." Qiao Yu explained angrily.

It was a normal thing, but when Qiao Xi asked it, it felt weird, as if there was some hidden secret between him and Teacher Lan.

"Old Xia! What can he talk to you about? Shouldn't I leave Coco to you now? I think it's a little cruel if you are only fifteen years old and have to raise two women." Qiao Xi dragged her. He raised his cheeks and commented. Qiao Yu felt that his face was going to turn dark.

He knew that his mother's mind was racing, but it was obviously getting worse recently.

"Comrade Qiao Xi, please face up to your family status! At my age, what normal parents fear most is their children falling in love early!" Qiao Yuyi said righteously.

Qiao Xi asked back: "Why do you think those parents are afraid of their children falling in love early? Aren't they just afraid of delaying their studies? So do you think falling in love early will delay your studies? You are not a normal child, why do you ask me to be a normal parent?" Qiao Yu sneered. , replied: "Is there a possibility that normal parents are not afraid of delaying their studies, but are afraid of causing trouble?"

This sentence clearly made my mother sitting on the sofa feel dazed for a moment.

This made Qiao Sha feel a little regretful. Just when he was about to speak, Qiao An said calmly: "It's okay. With your temperament, you definitely won't do it. Do you know what I'm most afraid of? You have a habit of calculating everything. , it’s so cold that you can’t even secrete any secretions. Are you really happy like this?”

Then, without waiting for Qiao Yu's reply, he waved his hand half-heartedly and said, "Okay, go and do your studies, and don't disturb me watching TV." Qiao Yu didn't say a word and got into his room dejectedly.

.

I feel very annoyed. I know that when I argue with my mother, he never gets the advantage, and he always talks meanly... His ability to control emotions is still a bit poor!

But you can't blame him completely. Qiao Xi probably knows how to let him break through the defense best.

Fortunately, learning makes people happy. When a person is immersed in those beautiful number theories, all unhappiness can disappear instantly. Who said he has no hormone secretion?

Now he is very happy when doing problems every day! Once he is immersed in it, he can feel the madness of those math people.

Especially the question he prepared today, which he found on a professional mathematics forum. According to the questioner, the poster who created this post, this is a particularly interesting number theory question. This forum was created by him unintentionally.

Found it in a search engine, hidden in a corner behind several pages.

If it hadn't happened that the math problem he searched for coincided with some posts in the forum, it would have been impossible to notice it.

Even the registration for this forum is different from ordinary forums.

I probably learned from a website that starts with B. If you want to register for this math forum, you have to answer questions, and they are all math questions.

Although it is impossible to ask big questions due to the website registration, after all, it is difficult for the system to automatically review big questions, but the threshold of fifty multiple-choice questions in mathematics is enough to make people feel a headache. Each question is worth two points, and the score must be 90

Only if you have more than 100 points can you successfully register as a member.

And only if you successfully register as a member and log in to the forum, you can browse the content of the posts in the forum. Otherwise, you can only browse the post titles one by one in the web interface.

So Qiao Yu spent half an hour during the day to successfully register. Then he saw this pinned post.

Qiao Yu clicked in and took a look. A bunch of big guys who were known as math geeks all gave thumbs up to the author of the question and said that this question was indeed very interesting!

You must know that in this forum, the math geek represents a title that can only be obtained by answering at least 80 math questions published in the forum after review. They are all very powerful math players. For example, those like him who have just registered

Newcomers only have the title of rookie.

Not even a math rookie, just a rookie!

If you want to get the title of math novice, you must first answer a question on a help-seeking post on the forum and be given a satisfactory label by the poster.

In the forum, I got the title of math geek, and then there was only one title of math guru. This kind of top-level title can be said to be extremely rare in the forum, and it doesn't often pop up. The big guy who happened to come up with the question was the one

He is known as a math master. So this seemingly simple question aroused Qiao Yu's interest early in the afternoon.

This is actually an equation that requires an integer solution. The equation specifically looks like this:

In the first step, Qiao Yu didn't need to think too much at all. After just one glance, he could conclude that this equation is most likely homogeneous. This means that if (a, b, c) is a special solution of the equation , then such as (7a, 7b, 7c) are its solutions. The reason is also very simple. Multiplying each variable by a constant will not change the structure of the equation. You only need the numerator and denominator learned in elementary school to eliminate this knowledge. Click and it will be taken care of.

So Qiao Yu used the method of common transfer terms to transform it into a polynomial function, added a coefficient t, and then obtained a Diophantine equation. An equation that looked very three-dimensional, but was actually only two-dimensional.

Yes, after this period of study, Qiao Yu has mastered the ability to restore the geometric definition of an equation in his mind. A three-dimensional equation generally defines a two-cone surface, and k n-dimensional equations are Define a d-dimensional manifold.

Specific to this question, this surface is formed by the rotation of a line passing through the origin. But at this step, after removing the denominator from the equation, Qiao Yu was a little dumbfounded. Apparently it became a cubic equation after deformation.

And it is also a cubic Diophantine equation.

Qiao Yu didn't know yet at this time that the difficulty of solving the Diophantine equation at different times was completely different.

According to the geeks in the mathematics forum, the first-order Diophantine equation can be solved by an individual. The second-order Diophantine equation can be solved only by elementary mathematics. But the third-order equation involves various esoteric theories and countless problems. Open question. As for the four...

What do you say? At present, it is a problem that normal people are unlikely to touch.

Simply put, as the power of this type of equation increases, the difficulty does not increase linearly, but increases logarithmically.

This is probably the reason why a bunch of math geeks praised the person who wrote the question. They used a seemingly simple equation to lay a big hole. It was just to give those newcomers to mathematics a little color. Well, people are actually all Much the same.

Even guys who are very good at mathematics still like to watch other people's fun, especially those who are new to the industry.

Coincidentally, Qiao Yu, who feels that his understanding of number theory has changed in recent times, has decided that he is going to get into trouble with this equation. Isn't it just about finding an integer solution?

He can definitely do it! ..

There is really nothing to say about the time that followed. The thing that worried Principal Zhang the most did not happen.

Although more and more people have come to him to ask about Qiao Yu in the past two days, the feedback is excellent - Qiao Yu really doesn't care about these garbage people who covet other people's good things every day. This also makes Zhang Tiejun completely relieved.

No matter what his character is, Qiao Yu is at least trustworthy.

On the afternoon of July 4th, the day when the third-year junior high school students returned to school to receive guidance from their teachers to fill in the application form, no one came, so Qiao Yu entrusted Lan Jie with full authority to help him handle the matter of filling in the application form. Just like that, it was July 6th, the time to fill in the application form. At the end, Qiao Yu’s volunteer application account has not been logged in twice.

When everything was settled, Zhang Tiejun finally put his heart back into his stomach. This time he was really stable!

Under his leadership, Tieyi Middle School also recruited a top student who has a chance to win the IMO gold medal.

Really, a month ago, Zhang Tiejun would not even have dreamed that such a good thing could happen to him. Of course, he had to keep a low profile at this time.

After all, Qiao Yu has not yet received his results, which makes Zhang Tiejun hope for the first time that time can pass faster. If it goes faster, it is best to fast forward this summer vacation directly to the start of the Orsay Provincial Examination League in September. It is best to fast forward

By June next year, if there is really good news that Qiao Yu won the IMO gold medal, it would be better if he got the gold medal with a perfect score.

Yes, Zhang Tiejun can't wait to see Qiao Yu represent Tie Yizhong and kill everyone. Unfortunately, time does not depend on the will of an individual.

For example, Qiao Yu, he now really hopes that time can pass slower and give him more time.

The reason why he was so quiet during this period was not only because he had reached an agreement with the school in advance, but also because he had trouble with that seemingly simple equation.

He once suspected that this question had no integer solution at all, but when he threw this conclusion on the forum, the question maker with the title of mathematics master actually came out and replied to him: "I will use my future mathematics to

Life is guaranteed, this question has an integer solution 100% of the time."

Below are a bunch of math geeks with various yin and yangs. For example:
To be continued...