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数论 >> 一般数论 >> 初等数论
Questions in category: 初等数论 (Elementary Number Theory).

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Posted by haifeng on 2019-07-28 23:12:54 last update 2019-07-28 23:34:22 | Answers (0) | 收藏


$4!+1==25==5^2$

$5!+1==121==11^2$

$7!+1==5041==71^2$

对于 $n!+1=m^2$, 除了上面的 $n=4,5,7$ 之外, 还有解吗?

$11!+1==39916801$ is a prime

 

 

References:

Richard K. Guy, Unsolved Problems in Number Theory, D25 Equations involving factorial $n$.