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欧拉猜想
作者:数学组 来源:数学组 日期:2013/10/16 0:00:00

1、欧拉猜想

是由欧拉提出,从费马最后定理引出的猜想。这猜想是说对每个大于2的整数n,任何n- 1个正整数的n次幂的和都不是某正整数的n次幂,也就是说以下不定方程无正整数解。

 

2推翻

这猜想在1966年被L. J. LanderT. R. Parkin推翻。他们找出n= 5的反例:

27^5+ 84^5+ 110^5+ 133^5= 144^5

1988年,Noam Elkies找出一个对n= 4制造反例的方法。他给出的反例中最小的如下:

2682440^4+ 15365639^4+ 18796760^4= 20615673^4

Roger FryeElkies的技巧用电脑直接搜索,找出n= 4时最小的反例:

95800^4+ 217519^4+ 414560^4= 422481^4

现在仍未知道当n> 5时的反例。 

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