This is a VERY VERY hard problem and has not been solved until recently by Andrew Wiles.
1) n=4 can be solved by infinite descent.
2) Kummer provided a proof for certain primes (this uses extensive algebraic number theory)
3) all natural numbers: the proof relies heavily on the theory of modular elliptic curves, and it is very hard to comprehend.
九章數學出版社、九章數學基金會版權所有 本網頁各鍊結標題及鍊結內容歸原權利人所有 Copyright 2000 ~2004九章數學出版社、九章數學基金會 本網站內所有文字及資料版權均屬九章所有，未經書面同意之商業用途必究 This web site was made with XOOPS, a web portal system written in PHP. XOOPS is a free software released under the GNU/GPL license.