Re: n! + 1 = k^2


matt271829-news@xxxxxxxxxxx wrote:
Earle Jones wrote:
Is there a largest n for which

n! + 1 = k^2 (k = integer)

Example: 7! + 1 = 71 ^ 2

earle
*

Various references indicate that this is an unsolved problem: the
example you give is the largest known, but it is not known if there are
any larger.

http://www.research.att.com/~njas/sequences/?q=25%2C121%2C5041 says
that there are no more terms with k^2 < 10^20000.

This came as a surprise to me. After reading the original post, I
suspected the answer could be obtained in 30 minutes or so, by
factoring
k^2 - 1, since n! contains a lot of 2's if n is big.

Certainly some things can be said about k? (Other than: k is odd and
probably a few other obvious things as well.)

--- Christopher Heckman

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