Chapter 81: The Core of Fermat's Conjecture (Part II)

"No matter what the test question is, if you want to verify it, you must understand it, this is true of ordinary test questions, and the same is true of Fermat's conjecture!"

At the beginning, Wang Ning's explanation was different, he did not directly verify it, but began to introduce Fermat's conjecture.

"What is the Fermat conjecture? Is it just that when n>2, the indefinite equation xn+yn=zn does not have an integer solution of xyz≠0? Of course, it doesn't stop there, it has a very interesting little story.

In 1637, the mathematician Fermat wrote next to the 8th proposition in Book II of the Greek mathematician Diophantus, edited by Baccher: Cuiusreidemonstrationemmirabilemsanedetexi.Hancmargini**iguitasnoncaperet. ”

On the whiteboard, Wang Ning wrote the first trace. However, this trace is not a verification process, but a set of Latin scripts.

This is the sentence that Fermat wrote himself, what did he write? In Chinese translation, it means: it is impossible to divide a cubic number into the sum of two cubic numbers, or a power of four into the sum of two powers of four, or to divide a power higher than a second power into the sum of two powers of the same power in general. I'm sure I've found a wonderful way to prove this, but unfortunately the blank space here is too small to write. This is a quote from Fermat, and it is also the only core of Fermat's conjecture, and it is this core that gave birth to Fermat's conjecture, one of the world's three major conjectures. ”

After a pause, looking at the scholars who had already listened to the gods, Wang Ning continued: "Since the birth of Fermat's conjecture in 1637, people have not been able to find proof of this conjecture, so it has attracted the interest of a number of well-known mathematicians. Over the past 300 years, mathematicians have devoted themselves to the proof of conjectures, which has given birth to many important mathematical concepts and branches.

For example, elliptic curves and modular forms in algebraic number theory, and Galois theory in group theory. More importantly, the Fermat conjecture led to the birth of the 'ideal number', which almost laid the foundation of algebraic number theory! In this respect, the Fermat conjecture is undoubtedly great! ”

Wang Ning has to admit that the birth of every great conjecture has a very important role in promoting the mathematical community. Whether it is the four-color conjecture or the Goldbach conjecture, which is still not fully proven, it has had a profound impact on the mathematical community since its birth.

It is precisely because world-class conjectures have too much influence on mathematics that few conjectures can be recognized by the mathematical community and thus go down in history. Undoubtedly, the soon-to-be-born Wang Ning conjecture is one of such world-class conjectures, and its greatness has triggered the birth of the mathematical mirror system, which has almost subverted the entire mathematical community.

In order to harness this great conjecture, Wang Ning must seize every opportunity to enhance his fame, otherwise, it is easy to be crushed by doubts from the mathematical community.

After a pause, Wang Ning continued: "This is the true meaning of Fermat's conjecture, it is not just a simple mathematical conjecture, even if it has been successfully verified, but his influence on the mathematical community still exists. Of course, you don't want to listen to me introduce the Fermat conjecture, nor is it a lecture on the Fermat conjecture, but you want to know how to verify it! ”

Sure enough, hearing Wang Ning's words, everyone nodded subconsciously. As one of the three major conjectures in the world, the greatness of the Fermat conjecture is undoubted. A group of students who are interested in mathematics don't know how Fermat's conjecture is, that is, the person who introduced it is Wang Ning, and the shock in front allows the top students to listen quietly. If it had been someone else, they would have been heckled a long time ago.

Wang Ning didn't care about the top students' expressions, smiled indifferently, and began to write on the whiteboard: "In fact, it is not difficult to prove Fermat's conjecture, you only need to prove that the equation x4+y4=z4, (x,y)=1 and the equation xp+yp=zp, (x,y)=(x,z)=(y,z)=1 (p is an odd prime) do not have an integer solution of xyz≠0. ”

After writing this, Wang Ning did not continue to write, but put down the pen, rubbed his wrist that was a little sore, turned around, and said to a group of top students: "This is the core verification of Fermat's conjecture, and then there is Fermat's final theorem as an integer n>." 2, the indefinite equation x^n+y^n=z^n. for x,y,z has no positive integer solution. If anyone is interested, you can find a computer and enter the research yourself!

"That's it?"

Seeing Wang Ning put the pen down, a group of scholars blinked their eyes and asked at a loss.

In the original ordinary test questions, the other party was able to write a whiteboard in different ways. And now they are not facing ordinary test questions, but the test questions on the whiteboard are the Fermat conjecture of the world's three major conjectures, and the other party wrote a few lines, and they don't know one of the lines. This is too perfunctory, isn't it?

In response to this question, Wang Ning shrugged his shoulders and said casually: "Yes, it's over." I have written the origin and core proof of Fermat's conjecture, do you have to write all the verifications? In that case, I'm sure you'll have to wait for me for a month! ”

No, it's normal to write the core verification method, but if you bring in the numbers one by one, it's the biggest trouble. What are the numbers? No one knows, but there is a special symbol for mathematics to illustrate, infinity. Numbers in mathematics are theoretically infinite, and numbers that meet the criteria of Fermat's conjecture are theoretically infinite.

If he wants to prove Fermat's conjecture thoroughly, even if there is an answer, Wang Ning has to write it for a month, and he is not prepared to do those stupid things. After reaching a certain level of mathematics, you can understand it naturally, and those who don't understand it, even if you write all the verification processes, they can't understand it.

Undoubtedly, there are more people who don't understand on the spot. All the top students almost didn't understand it, but it doesn't matter, there are people on the scene who can understand it anyway.

"Bang Bang Bang ......"

Just as the top students wanted to continue asking, a crisp applause came from behind them.

Interrupted by someone, all the top students couldn't help frowning slightly, and turned their heads to see who was so rude. An old man with a thin figure and an old face, but his face was still ruddy, appeared in their eyes.

"Shhh...... It turned out to be Professor Wu! ”

Wu Bingbai is one of the business cards of Yulan University of Technology, and many scholars have naturally seen his photos, and when they saw each other for the first time, they already recognized Wu Bingbai's identity.

found that the person who applauded was Wu Bingbai, and a group of scholars who were ready to ask for guilt all wilted. Wu Bingbai didn't dare to offend, what was even more exaggerated was that Wu Bingbai actually began to applaud, could it be said that the other party's verification process was correct? Just these few lines!!