The expression of Fermat's last theorem is simple: for positive integers, it is impossible to write a power higher than 2 times as the sum of two powers of the same power. In other words, the equation xn+yn = Zn has no positive integer solution when n > 2. In the margin of a book, Fermat wrote: I have a very beautiful proof of this proposition. The margin here is too small to write.
Since then, countless wise men, including great mathematicians Euler and Cauchy, have done their best for this. Although they can take a small step forward every time, they can't finally prove Fermat's last theorem. For more than 300 years, many people claimed to have found a solution to this difficult problem, but it was overturned every time. As far as Fermat's last theorem itself is concerned, proof is of little significance to the development of mathematics. But on the one hand, this is a challenge to wisdom; On the other hand, mathematicians have gained many unexpected gains in the process of proving Fermat's last theorem, and some new branches and methods of mathematics have emerged in the study of it. So the proof of Fermat's last theorem has always been proved by people.
Worries.
There are many episodes about Fermat's Last Theorem, among which German Paul Wolfskeil set up a special fund for Fermat's Last Theorem. According to people's popular saying, Wolfskeil tried to end his life because he was lovelorn. Some time before he thought everything was ready to shoot himself at midnight, he found a paper on Fermat's Last Theorem. As it happens, Wolfskeil himself is a math enthusiast, so he unconsciously got lost in the paper and missed the scheduled suicide time. Later, Wolfskeil gave up the idea of suicide and left a will before he died, giving a large sum of wealth as a prize to the first person who proved Fermat's Last Theorem, valid until 2007.
Andrew wiles, a professor at Princeton University, published his proof of Fermat's Last Theorem in 1993 after seven years of painstaking research. His certificate was confirmed on 1995, and he finally won the prize left by Wolfskell.
Wiles's proof is more than 100 pages, involving a lot of the latest mathematical knowledge, and only a handful of people in the world can understand it at present. So there is such a controversy: some people think that this can't be the proof that Fermat thought of in the past, and there should be a simpler proof that has not been discovered; But there are also many people who tend to think that Fermat didn't actually find anything, or just thought of a wrong method.
The problem is that when n>2, the indefinite equation X N+Y N = Z N has no positive integer solution. Mathematically, this is called Fermat's Last Theorem, which is also called "Book Edge Theorem" and "Fermat's Last Theorem". In order to get a positive or negative proof of it, generations of the best mathematicians have studied it several times in history, and even using modern electronic computers can only prove that Fermat's Last Theorem is correct when n is less than or equal to 465,438+0 million. At that time, Fermat claimed that he had solved the problem, but he did not publish the results, leaving a rare eternal mystery on this mathematical problem.
1On June 24th, 993, The New York Times, a world-recognized authoritative newspaper, published a news about solving mathematical problems. The headline of the news is "In the ancient mathematical dilemma, someone finally said" I found it ".
In the 1950s, Yutaka Taniyama, a Japanese mathematician, first put forward a conjecture about elliptic curves, which was later developed by Goro Shimamura, another mathematician. At that time, no one thought that this conjecture had anything to do with Fermat's last theorem. In 1980s, German mathematician Frey linked Yutai Taniyama's conjecture with Fermat's last theorem. What andrew wiles did was to prove that one form of Yutai Taniyama's conjecture was correct according to this connection, and then deduced Fermat's last theorem.
This conclusion was officially published by Willis at the seminar of Newton Institute of Mathematics, Cambridge University, USA on June 2 1, 1993. This report immediately shocked the whole mathematics field, and even the public outside the mathematics door paid infinite attention. However, wiles's certificate was immediately found to have some defects, so it took wiles and his students 14 months to correct it. 1September 1994 19 They finally handed over a complete and flawless scheme, and the nightmare of mathematics finally ended. 1In June 1997, wiles won the Wolfskeil Prize at the University of G? ttingen. At that time,100000 counterfeit goods were about $2 million, but when wiles received them, it was only worth about $50000, but andrew wiles has gone down in history and will be immortal.
Description:
Prove Fermat's last theorem is correct
(that is, x n+y n = z n for n > =3 has no positive integer solution)
It is only necessary to prove that x 4+y 4 = z 4, x p+y p = z p (p is an odd prime number) has no integer solution.
For a positive integer, it is impossible to write a power higher than 2 as the sum of two powers of the same power. In other words, the equation Xn+Yn=Zn, when n >; 2, there is no positive integer solution.
If Xo is the extreme point of the function f(x) and f(x) is derivable at this point, then f(x)=0.
The problem is that when n>2, the indefinite equation X N+Y N = Z N has no positive integer solution. Mathematically, this is called Fermat's Last Theorem, which is also called "Book Edge Theorem" and "Fermat's Last Theorem". In order to get a positive or negative proof of it, generations of the best mathematicians have studied it several times in history, and even using modern electronic computers can only prove that Fermat's Last Theorem is correct when n is less than or equal to 465,438+0 million. At that time, Fermat claimed that he had solved the problem, but he did not publish the results, leaving a rare eternal mystery on this mathematical problem.
1On June 24th, 993, The New York Times, a world-recognized authoritative newspaper, published a news about solving mathematical problems. The headline of the news is "In the ancient mathematical dilemma, someone finally said" I found it ".
In the 1950s, Yutaka Taniyama, a Japanese mathematician, first put forward a conjecture about elliptic curves, which was later developed by Goro Shimamura, another mathematician. At that time, no one thought that this conjecture had anything to do with Fermat's last theorem. In 1980s, German mathematician Frey linked Yutai Taniyama's conjecture with Fermat's last theorem. What andrew wiles did was to prove that one form of Yutai Taniyama's conjecture was correct according to this connection, and then deduced Fermat's last theorem.
This conclusion was officially published by Willis at the seminar of Newton Institute of Mathematics, Cambridge University, USA on June 2 1, 1993. This report immediately shocked the whole mathematics field, and even the public outside the mathematics door paid infinite attention. However, wiles's proof was immediately found to have some defects, so it took wiles and his students 14 months to correct it. 1September 1994 19 They finally handed over a complete and flawless scheme, and the nightmare of mathematics finally ended. 1In June 1997, wiles won the Wolfskeil Prize at the University of G? ttingen. At that time,100000 counterfeit goods were about $2 million, but when wiles received them, it was only worth about $50000, but andrew wiles has gone down in history and will be immortal.
Description:
Prove Fermat's last theorem is correct
(that is, x n+y n = z n for n > =3 has no positive integer solution)
It is only necessary to prove that x 4+y 4 = z 4, x p+y p = z p (p is an odd prime number) has no integer solution.