9th Irish 1996 Problem A1 Find gcd(n!+1, (n+1)!).
Obviously n! and n!+1 have no common factor. If n+1 is prime, then by Wilson's theorem n+1 divides n! + 1, so gcd(n!+1,(n+1)!) = n+1. If n+1 is not prime, then all its prime factors divide n! and hence do not divide n!+1, so gcd(n!+1,(n+1)!) = 1. Thanks to Dror Speiser 9th Irish 1996 © John Scholes jscholes@kalva.demon.co.uk 26 Nov 2003 Last updated/corrected 26 Nov 03