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Chapter 66: Shocking skills, full firepower (please subscribe, please vote)

As usual, Qiao Yu stood outside the building and watched Principal Zhang and Teacher Lan disappear from his sight before turning around and going home.

For him, doing so shows respect for the guests and costs almost nothing.

Qiao Yu's principle is to avoid leaving bad impressions when you can leave a good impression on useful people. It is certainly nice to show your personality, but if it conflicts with the potential benefits you may gain, then it is better not to show your personality for the time being.

Being the most handsome guy in the eyes of passers-by for a while can only satisfy your illusory vanity.

No matter how nice the words of passers-by sound, they cannot change his life. But the money in his pocket is a real good thing.

Merchants are unlikely to give discounts to customers just because they have unique personalities, but they may give customers broken bones because the customers have too much unique personality.

Qiao Yu has always felt that the biggest advantage of a country with a long history is that the ancients have almost summed up all kinds of life experiences. For example, the first bird to stick its head out gets shot, and the tree that stands out in the forest will be destroyed by the wind.

In short, personality should be like ability. Show it when it is time to show it, and hide your shortcomings when it is time to hide them.

……

As Qiao Yu turned around and walked into the building, he happened to meet Xia Hongliang who was walking down the stairs carrying a garbage bag.

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

The idea was good, but he was stopped by an adult: "Qiao Yu, did you just send your principal Zhang away?"

"Yeah." After saying that, Qiao Yu wanted to slip away again, but was stopped again: "Wait, I'll throw away the garbage, let's chat for a while. It won't take up much of your time."

Qiao Yu thought about it and decided to stand at the entrance and wait.

The trash can for each unit is not far from the building. It didn't take long before Old Xia came back. He then skillfully took out a pack of cigarettes from his pocket, put one in his mouth, and was about to put it back in his pocket when he thought of something, took out the cigarette again, knocked out half of it, and handed it over.

"Do you want?"

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

"Don't pretend. I've seen you smoke before." Old Xia glanced at Qiao Yu and said.

Qiao Yu shook his head and said, "I'm not pretending. I did smoke before, but I quit last month."

"Oh? Don't say that it was Coco who asked you to quit." Old Xia couldn't help but tease.

Qiao Yu shook his head again and said, "No, it was that teacher Lan. He said that if I want to participate in IMO, I must quit smoking. Otherwise, he won't take me to play."

Old Xia is a little bored.

It’s not because Qiao Yu chose to quit smoking not 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 were impetuous and had too many new words.

Fortunately, Qiao Yu probably figured out something and took the initiative to explain: "IMO is the abbreviation of International Mathematical Olympiad. There's nothing we can do about it. People who speak Indo-European languages ​​like to use abbreviations, which makes people feel confused."

Old Xia was stunned for a moment, then silently put the cigarette back into his pocket, took out his lighter and lit it for himself, took two deep puffs, and then said self-deprecatingly: "You are a ruthless person, you can quit smoking just by saying so, but I'm afraid I can't quit smoking in this lifetime, and I get scolded by your Aunt Liu every day for this."

Qiao Yu smiled and flattered, "That's because you often have to work night shifts, so you need to refresh yourself. If you were really transferred to guard the train every day, you would be able to quit. People's habits are forced out."

Old Xia smiled. This kid is still as smart as before and always speaks so nicely.

"Come on, you know that Uncle Xia, I am a rough man. I have never had good grades since I was young. I was able to enter the railway because of my father's position. This is probably how my life will be. I won't achieve much.

Unfortunately, this crappy class is full of things to do and takes a long time. I have to follow the car for several days. I only have one daughter, and I can't take care of her. Fortunately, Keke is doing well. In fact, I have to thank you. If it weren't for you, Keke might not be so hardworking. "

Qiao Yu smiled politely. It was not easy for him to respond to this, especially since he could not judge the middle-aged man's intentions.

"It's just that now this girl doesn't really listen to me and her mother anymore, she only listens to you. I'm not saying that's a bad thing, it's just that this girl has a bit of a weird temper, just like her mother, and sometimes she's really annoying. If she annoys you in the future, give Uncle Xia some face and don't let her lose face."

Old Xia said very humbly.

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

Old Xia finally smiled on his weathered face. He took a last puff and flicked the cigarette butt away without any manners. Then he reached out and patted Qiao Yu on the shoulder. "That's enough for you to say. Let's go home."

……

After returning home, Qiao Xi looked him up and down in surprise again.

"What's wrong again?" Qiao Yu asked in confusion.

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

"When I came back, I ran into Uncle Xia who was going downstairs to throw away the trash. He pulled me aside to chat for a few minutes." Qiao Yu explained unhappily.

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

"Old Xia! What can he talk to you about? Shouldn't I entrust Coco to you now? You are only fifteen years old, and you have to support two women. I think it is a bit cruel." Qiao Xi commented, holding his chin.

Qiao Yu felt his face turn black.

He knew that his mother's thoughts jumped, but recently they had obviously jumped more frequently.

"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 Yu said righteously.

Qiao Xi asked back: "Why do you think those parents are afraid of their children falling in love too early? Aren't they afraid that it will affect their studies? So do you think falling in love too early will affect your studies? You are not a normal child, why do you ask me to be a normal parent?"

Qiao Yu sneered and retorted, "Is it possible that normal parents are not afraid of delaying their studies, but are afraid of causing a death?"

This one sentence obviously made my mother, who was sitting on the sofa, dazed for a moment.

This made Qiao Yu feel a little regretful. When he was about to open his mouth to make amends, Qiao Xi said nonchalantly, "It's okay. With your cautious nature, you definitely won't do that. Do you know what I'm most afraid of? You habitually calculate everything every day, and you're so calm that your hormones are not even secreted. Are you really happy like this?"

Then, without waiting for Qiao Yu to reply, he waved his hand in a disinterested manner and said, "Okay, go and study, don't disturb me watching TV."

Qiao Yu said nothing and went into his room dejectedly.

I was very upset. I knew that he would never get the upper hand in an argument with his own mother, but he still kept saying mean things...

My ability to control my emotions is still a little lacking!
But we can't blame him entirely, Qiao Xi is probably the one who knows best how to break his defense.

Fortunately, learning makes people happy. When people are immersed in the beautiful number theory, all the unhappiness will disappear in an instant.

Who said he has no hormones?

Now he is very happy when doing the questions every day! Once you immerse yourself in it, you can feel the madness of those mathematicians.

Especially the question he prepared today, which was found on a professional mathematics forum. According to the person who set the question, that is, the author of this post, this is a particularly interesting number theory question.

He found this forum by accident, hiding in a corner behind several pages of the search engine.

If the math problems he searched for didn't happen to coincide with some posts in the forum, it would have been impossible for him to be noticed.

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

Probably inspired by a certain website starting with B, if you want to register on this math forum you have to do some exercises, and they are all math exercises.

Although it is impossible to come up with 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 math multiple-choice questions is enough to give people a headache.

Each question is worth two points, and the score must be above 90 points to successfully register as a member.

Moreover, only after successfully registering as a member and logging into the forum can you browse the contents of the posts in the forum.

Otherwise, you can only browse the post titles one by one on the web interface.

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

Qiao Yu clicked on it and saw that a bunch of math geeks gave the poster a thumbs up and said that the question was really damn interesting!

You should know that in this forum, math geeks are those who have answered at least 80 math questions that have been reviewed and posted on the forum. They are all very capable math players.

For example, a newcomer like him who just registered only has the title of a rookie.

It's not even a math rookie, it's just the word "rookie"!
If you want to get the title of math rookie, you must first answer a question in a help post on the forum and be given a satisfactory label by the poster.

After earning the title of math geek in the forum, the next highest title is math expert, which is extremely rare in the forum and does not appear often. It just so happens that the guy who asked the question has the title of math expert.

So this seemingly simple question piqued Qiao Yu's interest early in the afternoon.

This is actually an equation that requires integer solutions.

The equation looks like this:

Qiao Yu didn't need to think too much at the first step. He only needed to take a glance to conclude that the equation was most likely homogeneous. This means that if (a, b, c) is a particular solution of the equation, then (7a, 7b, 7c) are all its solutions.

The reason is very simple. Multiplying each variable by a constant will not change the structure of the equation. It can be handled by simply canceling out the numerator and denominator learned in elementary school.

So Qiao Yu used the method of common denominator and transposing terms to transform it into a polynomial function, added a coefficient t, and then obtained a Diophantine equation.

An equation that looks very much like three-dimensional, but is 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 when he sees it.

A three-dimensional equation generally defines a two-cone surface, while k n-dimensional equations define a d-dimensional manifold. In this case, the surface is formed by rotating a line through the origin.

But at this point, after removing the denominator from the equation, Qiao Yu was a little dumbfounded.

Obviously after deformation it becomes a cubic equation.

And it's a cubic Diophantine equation.

Qiao Yu didn't realize at this time that the difficulty of solving the Diophantine equation of different degrees is completely different.

To use the words of those weirdos in math forums, a linear Diophantine equation can be solved by anyone, and a quadratic equation can be solved using only elementary mathematics methods, but when it comes to the third order equation, it involves all kinds of profound theories and countless open problems.

As for the four times...

What can I say? For now, it is unlikely that normal people will try to scam someone.

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

This is probably why a bunch of math geeks praised the person who came up with the question. He used a seemingly simple equation to create a big trap. It was just to teach those math newbies a lesson.

People are actually all the same.

Even guys who are good at math like to watch other people having fun, especially those who are new to the industry.

Coincidentally, Qiao Yu, who felt that his understanding of number theory had greatly improved in recent times, had decided that he would take on this equation.

Isn’t it just finding the integer solution?

He can definitely do it!
……

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

Although more and more people have come to him to ask about Qiao Yu in the past two days, the feedback has been very positive - Qiao Yu really doesn't pay any attention to these rubbish people who covet other people's good things every day.

This also made Zhang Tiejun completely relieved.

No matter what Qiao Yu's character is, at least he is trustworthy.

On the afternoon of July 4, the day when the third-year junior high school students returned to school to receive guidance from teachers to fill in their applications, Qiao Yu did not show up, and fully entrusted Lan Jie to handle the application for him. In this way, on July 6, when the application period ended, Qiao Yu's application account had not been logged in again.

Now that everything has been settled, Zhang Tiejun can finally put his heart at ease.

This time it’s really stable!
Under his leadership, Tieyi Middle School also recruited a top student who had the opportunity to win the IMO gold medal.

Really, a month ago, Zhang Tiejun wouldn’t even dare to dream that such a good thing would happen to him.

Of course, you have to keep a low profile at this time.

After all, Qiao Yu's results were not out yet. This made Zhang Tiejun hope for the first time that time would pass faster and faster. It would be best if he could fast forward to this summer vacation and go straight to the start of the provincial Olympic examination league in September. It would be best if he could fast forward to next June and hear the good news that Qiao Yu had won the IMO gold medal, and it would be best if it was a gold medal with full marks.

Yes, Zhang Tiejun can’t wait to see Qiao Yu represent Tieyi Middle School to wreak havoc.

Unfortunately, time cannot be changed by individual will.

For example, Qiao Yu 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 reached an agreement with the school in advance, but also because he was struggling with that seemingly simple equation.

He once suspected that this question had no integer solution at all, but when he posted this conclusion on the forum, the questioner who was known as a math expert actually popped up and replied to him: "I guarantee with my future mathematical life that this question has 100% integer solution."

There are also a bunch of math geeks below with all kinds of yin and yang.

such as:

"No way? There are really newcomers who would pick such a cheap topic?"

"Young man, your courage is really commendable, but mathematics is not about brute force, it requires brainpower! For example, when I take a look at this kind of question, my brain tells me to stop trying! You can't do it!"

"Are you a freshman in a mathematics school or research institute this year? Did your supervisor recommend you? Let me tell you, these number theory problems that require integer solutions are not as simple as they seem. Listen to my uncle's advice. The first step to learning real mathematics is to learn to let go. Accepting the fact that you are mediocre is a necessary process on your path to mathematics. Remembering this is more important than anything else."

……

Seeing these ridicules, Qiao Yu became even more dissatisfied.

Although he didn't quite understand how credible it was that the math guru said that future mathematical life would guarantee that this problem had an integer solution, since everyone believed that this problem had an integer solution, he really decided to compete with this problem.

This was his fifth day of trying to solve the equation.

Although Qiao Yu did not spend all his time solving problems every day, he still watched videos in the morning and spent the afternoon doing exercises related to the content of the video, but in the evening, Qiao Yu really kept struggling with this equation.

It was because of this question that he was unable to maintain the good work and rest habits he had just developed. He would think until two or three in the morning.

This is probably also related to the fact that the cram school that Xia Keke signed up for officially started on July 8th.

The cram school has a similar schedule to junior high school, with classes starting at 7:30 in the morning, so after the 8th, it would be impossible for Xia Keke to wake Qiao Yu up at 8 o'clock every morning for breakfast.

It is indeed very hard to live this kind of life during the summer vacation, but if your goal is to go to Huaqing University or Peking University, and unless you are gifted, you have to persevere no matter how hard it is.

After all, there are many students who suffer worse than the 996 office workers in high school. Not to mention that those who work 996 can still find time to slack off and deceive their leaders. Choosing to slack off in high school is purely deceiving yourself.

It’s just that high school is only three years long, so you have expectations and can see the end. Once you enter society and choose to start working 996, you really don’t know how many years it will take for the work to end.

It's actually the same for Qiao Yu.

Even if you go to bed at three in the morning, you must get up at nine in the morning. After all, studying in the morning is very necessary.

In this way, Qiao Yu spent a full ten days, and finally with the help of the desktop computer at home, he finally solved the equation at 8:30 in the evening on July 12.

Then he couldn't help but curse out loud: "Fuck!"

God helps those who work hard, he finally solved the damn equation, and after substituting it into the equation for verification, he found that the equation's equation relationship is indeed valid.

But the answer is exaggerated.

Because the values ​​of the three variables a, b, and c all reach eighty digits!

The end result is:
a=154476802108746166441951315019919837485664325669565431700026634898253202035277999,

b=36875131794129999827197811565225474825492979968971970996283137471637224634055579,

c=4373612677928697257861252602371390152816537558161613618621437993378423467772036.

Qiao Yu finally understood how stupid this question was and how dirty the heart of the math expert who gave this question was!
If he didn't have a computer and knew a little about programming, it would be impossible for him to figure it out!

As we all know, this type of problem cannot be solved directly by using computer brute force calculations, even if two variables have been determined, because the total number of combinations to verify that the third variable is an integer is 10 to the 160th power.

According to the peak computing power of 12.5 quadrillion times of a large Chinese supercomputer, it can only perform 10 to the 18th power calculations per second. In order to solve this problem, it will take 10 to the 134th power years.

So we must first find a solution to this problem.

In order to solve this problem, Qiao Yu really reasoned about too many things. He even used up a lot of scratch paper just to draw the elliptic curve.

The methods tried included special value substitution, Euclidean algorithm, modular operation, approximation and approximation, mean inequality... and more than ten sleepless nights!

Fortunately, no matter how tortuous the process was, he finally solved it!

So Qiao Yu quickly logged onto the forum, and with high spirits and the title of rookie, he directly created a new thread.

"That equation that you all said was difficult and impossible to solve was solved by this rookie!"

Then he quoted the original question, copied and pasted the answer directly, and simply @ed the poster who asked the question.

"Okay, I admit that I was superficial before. You are right. This problem does have a solution. I have found the integer solution and verified it. The answer is now published as follows... In addition, I want to respond to some people's previous comments.

Thanks to the senior who said that math is not about brute force but about brains. It turns out that I have brains too. But I wonder, if your brain tells you to stop after just a glance, does it mean that your brain thinks your IQ is not high enough, so it triggers the alarm to let you back off?

But I'm really sorry, when I saw this question for the first time, my brain told me with certainty that the solution to this question is as simple as the question itself. As long as you are willing to solve it, you will definitely be able to solve it!
Now it seems that my brain is right! Oh, by the way, I also want to thank the uncle who tried to tell me that the first lesson in learning mathematics is to learn to give up! Maybe you are talking about your life experience and accepting your mediocrity, but obviously, your life experience does not apply to me!

Maybe what I said will make you seniors angry, but please don't be angry yet. I came to this forum, and you old guys will have many opportunities to get angry in the future! I am afraid that you will get angry now and it will be difficult for you to set questions in the future.

If you are not convinced, you can continue to talk to me with mathematics, and I will continue!"

……

After posting, Qiao Yu felt refreshed, then jumped onto the bed and fell asleep instantly.

In reality, he could only obey orders for the sake of dozens or hundreds of red papers simply because he was forced by life.

Once you get on the Internet, I'm sorry, if you're unhappy you'll have to strike back hard.

Anyway, those random netizens on the forum don't know him and won't affect him at all. He should look down on others when he should.

So, as expected, Qiao Yu’s new post went viral!

No, it should be said that half of the Chinese number theory community was boiling with excitement!
(End of this chapter)