Prove that n!-1 is a composite number when n>3 and n+2 is a prime.
let n+2=A and let n!-1=B
now let P1,P2,....,Pk be all the primes less than or equal to A-2
now from (1) be get that B+1 is divisible by all of P1,P2,...,Pk thus B is congruent to (Pk-1) mod Pk for all Pk
this is where I am stuck, if anybody can offer some assistance I would greatly appreciate it.
My instincts tell me that B+1 being divisible by a bunch of consecutive primes forces B to be composite but I'm having problems proving it
Posted by Daniel
on 2007-01-24 10:34:13