I Am the President of the University

"I'm the president of the university(!

[Recursive sequence of integer points on elliptic curve and solution by quadratic residue method]

【Abstract: The congruence properties of a special type of recurrence sequence are studied. Using these properties and the methods and techniques of elementary number theory such as quadratic residues, it is proved that all the integer points of the elliptic curve y2=x3-30x+133 proposed by Zagier are (x, y)=(-7, 0), (-3, ±14), (2, ±9), (6, ±13), (5143326, ±11664498677). 】

[Keywords: Diophantine equation; elliptic curve...]

Lu Zhou steadily typed on the keyboard with both hands, and saw more and more words on the computer screen, and in a short while, he filled the first job in the document.

Number theory is one of the branches of pure mathematics, which mainly studies the properties of integers. Integers can be solutions of equations (Diophantine equations). Some analytic functions (like the Riemann ζ function) include the properties of integers and prime numbers. Through these functions, we can also understand some number theory problems.

The source of this mathematics paper is that when he was studying number theory, he noticed the integer point problem of elliptic curves. Due to the diversity of curve types, there is no unified method or algorithm that can solve any given number within a finite step. The integer points of the elliptic curve.

How to solve this integer point problem?

Lu Zhou's brains flashed, and he transformed the integer point problem of elliptic curves into the number theory properties of the recurrence sequence, and finally used the elimination method to find all integer points.

Although the recursive sequence method is a kind of elementary method, it can solve some difficult Diophantine equation solving problems by combining with the quadratic residue and using certain skills.

"In order to prove Theorem 1, it is necessary to study the congruence properties of the recurrence sequence. It is calculated that 649+180√13 is the Pel equation..." Lu Zhou whispered while writing the paper.

The roommate Pharaoh on the side didn't know where he leaned forward, arched his waist slightly, looked at the computer screen very curiously, and asked suspiciously: "Elbow, are you doing homework or what?"

"Write a essay." Lu Zhou replied without looking away from the computer.

"Thesis and thesis, do you want to submit it?" Lao Wang said with wide-eyed eyes and a little squat.

"Of course it is to be submitted, otherwise, why do you write it?" Lu Zhou paused for a while, and then continued the keyboard sound again.

"Contribution! This is a legendary paper submission. What a great feeling!" Lao Wang immediately stared at Venus. To a sophomore student, he always said that he had never touched the paper, and it was usually a course of writing homework. The paper is completely different from this kind of real paper.

Probably most undergraduates will come into contact with this only when they are writing their graduation thesis after four years.

"Isn't this a mathematics paper?" Lao Wang took a few glances, and then thought of Lu Zhou, who had won the National College Students Mathematical Modeling Competition, the Higher Education Club Cup, and he was extremely talented in mathematics.

"Yes, it's mathematical."

"Too awesome!"

Lao Wang spoke with some admiration, and then he leaned close to recite the question, "The recursive sequence of integer points on the elliptic curve...what is this? Why can't I understand it at all."

Lao Wang's eyes were suddenly blurred, let alone the content, the title of a paper has already stunned him.

"It's normal to not understand." Lu Zhou said casually.

Lao Wang got up and stood behind Lu Zhou, looking enviously at Lu Zhou's back.

There is only envy, no jealousy or hatred.

Living together every day, he knew how hard Lu Zhou was in his studies and how much sweat he had put in.

It is only natural to have achieved achievements now.

With talent and such hard work, such a person is unsuccessful to hell.

"I want to be as motivated as Lu Zhou!"

The thought that popped out of his mind startled him.

But immediately, he was a little moved.

"Why don't you try?" he asked unconfidently.

Thinking about it, Lao Wang went back to his seat, took out the book and started reviewing.

A roommate next to him happened to go to the bathroom and noticed Lao Wang's abnormality. He couldn't help but ridicule: "Oh, why is Lao Wang still starting to learn? Isn't it the end?"

"While going, don't disturb my self-study, please ask me to learn Bawang from now on!" Lao Wang said confidently.

ten minutes later.

Pharaoh started fighting with his upper and lower eyelids, and the frequency of yawning was as high as seven or eight times in one minute.

"Pharaoh, is my king's pesticide? 4 missing one, just waiting for you, will you come?" shouted the roommate.

"Don't fight...I'm studying." Old Wang said with a yawn.

"I really won't come, there are sister papers!" The roommate smiled.

"No, there is a golden house in the book, and Yan Ruyu in the book!" Lao Wang said firmly.

"Cut, you will only be hot for three minutes, and I will persuade you if I can hold on for a day."

After seeing no results, the roommate directly pulled a savage and started.

Fifteen minutes later.

Lao Wang turned his head to the roommate he had invited before, hesitated, and asked, "Achun, have you finished the fight?"

"What are you doing, didn't you look for your Yan Ruyu?"

"Ahem, Yan Ruyu seems not to be at home today. I'm studying. It's okay to study later. I'll play games with you before going to study." After the old Wang finished speaking, he threw the book away, and took a chair to sit next to his roommate. .

Seeing this scene, Lu Zhou couldn't help but shook his head.

As for people, most of them are three-minute enthusiasm, or fake diligence.

Learning is not an easy task, and it is a long-term task that must be persevered, but most people will give up halfway.

Lu Zhou was very firm in his beliefs. He wanted to see where his limits were and how vast the world was.

...

Guanghua University's Pulan Café.

At 8 o'clock in the evening, it was already pitch black outside. Fortunately, the street lights on both sides of the road were on, which didn't seem so lonely.

"Principal." X3

Three voices sounded one after another. Chen Hao nodded slightly and said with a smile: "There will be a group meeting in the big evening. Didn't it cause you trouble?"

"No, but the principal, you are too dedicated..." Li Qiubai said with emotion.

The principal of the big evening hasn't gone back yet, staying in school, how many other people's universities can have.

"Fortunately, life is fulfilled, and it's good to be busy."

The coffee I ordered came up just then.

The waiter put down the four cups of coffee and said politely, "Hello, your four cups of coffee, please enjoy it slowly."

Looking at the coffee on the table, Chen Hao waved his hand and waved: "I don't know what you like to drink. Anyway, I ordered American, cappuccino, latte, and mocha. You're welcome, just take it directly."

At the end of hearing, the three of them looked at each other, but Song Qingtong stretched out his hand first and unceremoniously chose a cup of coffee.

After Wei Shu finished the election, there was no one to choose the American style.

Several people drank coffee and started chatting.

"Tonight, I asked you to come out for a group meeting, mainly because the course guidance documents of the pilot class have also come out. Do you have any comments after reading it?" Chen Hao took a sip of coffee and asked with a smile.

The three of you look at me, I look at you, the last person who spoke was Li Qiu white man.

"Principal, after reading the documents, I am fine with professional courses and elective courses, but is this general education too much?" Li Qiubai said depressed.

There are 12 professional courses and 10 elective courses, but there are 14 general education courses.

This is very wrong. How can there be more general education courses than professional courses?

"The 14th period is okay. If it weren't for the fear of giving you too much class, it might be more than 14th period." Chen Hao said with a light smile.

Li Qiubai:...

"Principal, can I take less of this general education course? I'm only interested in computers, and you know it." Li Qiubai looked at Chen Hao and said in a discussing tone.

"I picked out the three of you. Of course, the main computer has potential." Chen Hao said, changing the topic. "General education courses are still very useful. You can combine your general education courses with your own professional fields. Linking up is a process of finding out and filling up vacancies, and it is also a process of pursuing a higher level."

"Principal, is there really no way to change it?" Li Qiubai gave a wry smile.

Originally, I studied computer hard, but now 14 general education classes suddenly popped up, making Li Qiubai's plan unable to keep up with the changes.

"Of course not. This is a set rule. You can't make an exception at will." Chen Hao shook his head.

Why he formulated this general education course is to cultivate students' all-round ability, and to spread the thinking ability, so that when thinking about things, he can stand at a different angle and have multiple understandings.

"Well... then I'm fine." Li Qiubai sighed silently.

Wei Shu was very quiet for the remaining two people. Song Qingtong looked at it, and that was only himself.

After thinking about it, Song Qingtong asked, "Principal, it's already in early November. Will it be too late to select courses again?"

When these words came out, Li Qiubai's eyes also burst into light, apparently speaking in his heart.

"This is not a problem. For the students in the experimental class, waiting for you to choose a major, after the statistics are completed, we will set up courses for you separately according to the courses that the students hope to take." Chen Hao put down his coffee lightly and looked at the three of them and said.

"Is it like this? What if the school that a classmate wants to choose doesn't?" Song Qingtong suddenly thought of this and asked curiously.

"If the school does not have this course, then recruit people! The experimental class is a reform of the school's system, so it will attach great importance to the training of the experimental class, you can rest assured." Chen Hao explained.

The three looked at each other, no matter what, at least they could feel the sincerity of the school.

Not to mention that students in a class can make courses individually, but also because students go to create new courses, people have nothing to say.

"The Q&A is also over. I also have a little opinion about the arrangement of your courses. If you feel inappropriate, you can communicate together." With that, Chen Hao formulated the courses for the three of Li Qiubai in the past two days.

"Freshman year: last semester (General History 5, Elective 1), next semester (General History 5, Elective 1)

Sophomore: last semester (major 3, elective 2, general education 2), next semester (major 3, elective 2, general education 2)

Junior three: last semester (major 3, elective 2), next semester (major 3, elective 2

"In this way, you have just completed 36 standards in 3 years, and the credits are more than enough. I don't recommend that you take too many courses. You can't exceed 7 lessons in a semester." Chen Hao seriously reminded, "Learning lies in mastery and essence, and It's not about more, I hope you can all learn the course thoroughly."

Regarding the arrangement of this course, I discussed it for a while.

The group meeting started at 8 o'clock in the evening and didn't end until after 9 o'clock in the evening.

...

The next morning ~www.novelmtl.com~Beijing.

At Beijing University of Aeronautics and Astronautics, an anger sounded from the secretary's office.

The loud voice even attracted the attention of many school staff passing by.

"Professor Fang, I disagree!"

ps: I haven't written it yet. I will fill it up at noon tomorrow. I write that it is too sleepy at four o'clock and it is not efficient. Sorry everyone, alas, blame me for my inefficiency.

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