阶乘加1为平方数

manthanein

比如说：
\(4!+1=5^{2}\)
\(5!+1=11^{2}\)
\(7!+1=71^{2}\)
只有这三个解吗？

manthanein

原来1876年就有人提过了
http://math.fau.edu/richman/Interesting/WebSite/Number71.pdf

Brocard’s problem (1876) is to find numbers m such that m! + 1 is a square. Only
three such numbers m are known, 4, 5, and 7. For the largest of these, the square is
712 = 7! + 1. So 71 is the largest number known whose square is a factorial plus one. A
search by Berndt and Galway in 2000 showed that there are no further numbers m with
fewer than nine digits. Thus any number greater than 71 whose square is a factorial plus
one must have over 90;000 digits.

manthanein

https://en.wikipedia.org/wiki/Brocard%27s_problem