纪录片《费马最后的定理》 第04期 没有写出来的证明

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 brilliance¹, he scribbled² 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 margin³ 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。

1 brilliance   

n.光辉，辉煌，壮丽，（卓越的）才华，才智

参考例句：

• I was totally amazed by the brilliance of her paintings.她的绘画才能令我惊歎不已。
• The gorgeous costume added to the brilliance of the dance.华丽的服装使舞蹈更加光彩夺目。

2 scribbled   

v.潦草的书写( scribble的过去式和过去分词 )；乱画；草草地写；匆匆记下

参考例句：

• She scribbled his phone number on a scrap of paper. 她把他的电话号码匆匆写在一张小纸片上。
• He scribbled a note to his sister before leaving. 临行前，他给妹妹草草写了一封短信。

3 margin   

n.页边空白；差额；余地，余裕；边，边缘

参考例句：

• We allowed a margin of 20 minutes in catching the train.我们有20分钟的余地赶火车。
• The village is situated at the margin of a forest.村子位于森林的边缘。