>For any number a, 1<a<=n, n! mod a == 0; therefore, n!+1 mod a == 1. n!+1 >is prime. Prime numbers don't have integral square roots.
For example :
(4!+1)^(1/2)=5 (5!+1)^(1/2)=11 (7!+1)^(1/2)=71
I am completely wrong. I replied too hastily. Please accept my apologies. In fact, n!+1 is relatively prime to any a, 1<a<=n, however plainly it is much larger than n itself and when n>3, (n!+1)>(n^2) and may have factors (including an integral square root) larger than n. Oops :-) Scott Collins | "That's not fair!" -- Sarah | "You say that so often. I wonder what your basis 408.862.0540 | for comparison is." -- Goblin King ................|.................................................... BUSINESS. fax:974.6094 R254(IL5-2N) collins@newton.apple.com Apple Computer, Inc. 5 Infinite Loop, MS 305-2D Cupertino, CA 95014 ..................................................................... PERSONAL. 408.257.1746 1024:669687 catalyst@netcom.com