Fermat's last theorem: when the integer n > 2, the indefinite equation x n+y n = z n about x, y and z has no positive integer solution. Proof Method In 1950s, Yutaka Taniyama, a Japanese mathematician, first put forward a conjecture about elliptic curves, and later Goro Shimamura, another mathematician, developed this conjecture. 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 was also correct. 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 mark was about $2 million, but when wiles received it, it was only worth about $50000. However, andrew wiles has been recorded in the history books and will be immortal. Expressed by indefinite equation, Fermat's last theorem is: when n >; 2. The indefinite equation x n+y n = z n has no integer solution of xyz≠0. In order to prove this result, we only need to prove the equations x 4+y 4 = z 4, (x, y) = 1 and x p+y p = z p, (x, Y) = (X, Z) = 65438+. The case of n = 4 has been solved by Leibniz and Euler. Fermat himself proved that p = 3, but the proof was incomplete. Legendre [1823] and Dirichlet [1825] proved the case of p = 5. 1839, Lame proved the case of p = 7. 1847, the German mathematician Cuomo made a breakthrough in Fermat's conjecture. He founded the ideal number theory, which made him prove that when P