x的n次 + y的n次 = z的n次

n . x . y . z 為正整數 ; n 大於等於 3

試問""怎麼證明不可能有x的n次 + y的n次 = z的n次 "" ?

回應

昨天才看書看到 那叫做費曼的最後定理 它發表之後350年才有人終於用2個日本人的新定理(谷山-志村定理)解出來就是懷爾斯拉
可惜他最後沒有得菲爾茲獎 解出當時他42歲@@晚了2年
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.