纪录片《费马最后的定理》 第04期 没有写出来的证明（在线收听）

X squared plus y squared equals zee squared, and you can ask:

x²+y²=z²，你可以问：

well what are the whole numbers solutions of this equation?

那么这个等式的整数解是什么?

And you quickly find there's a solution 3 squared plus 4 squared equals 5 squared.

你很快就会找到一个答案是3²+4²=5²。

Another one is 5 squared plus 12 squared is 13 squared, and you go on looking and you find more and more.

另个答案是5²+12²=13²，继续寻找，你会找到越来越多的整数解。

So then a natural question is, the question Fermat raised:

一个自然而然的问题，也是费马提出的问题是：

supposing you change from squares, supposing you replace the two by three, by four, by five, by six, by any whole number 'n',

假设改变次方数，假设将平方改为三次方、四次方、五次方、六次方，以及任何整数'n'次方，

and Fermat said simply that you'll never find any solutions,

费马说仅如此，你就找不到任何解，

however far you look you'll never find a solution.

不管你怎么找，你永远也找不到一个解。

You will never find numbers that fit this equation, if n is greater than 2.

如果n大于2，你永远也找不到符合这个等式的数字。

That's what Fermat said, and what's more, he said he could prove it.

那正是费马所声称的，此外，他说他可以对之进行证明。

In a moment of brilliance, he scribbled the following mysterious note.

灵智闪现之时，他写下了如下神秘的话语。

Written in Latin, he says he has a truly wonderful proof "Demonstrationem mirabilem" of this fact,

他用拉丁文写道，关于这一事实他有了一个确实了不起的证明，"Demonstrationem mirabilem"，

and then the last words are: "Hanc marginis exigiutas non caperet", this margin is too small to contain this.

他最后语句是: "Hanc marginis exigiutas non caperet"，这空白处太小了，写不下。

So Fermat said he had a proof, but he never said what it was.

因此费马说他有个证明，但他从没有说出来那是什么。