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
n=A2
(A2)!1=B
(1) (A2)!=B+1
now let P1,P2,....,Pk be all the primes less than or equal to A2
now from (1) be get that B+1 is divisible by all of P1,P2,...,Pk thus B is congruent to (Pk1) 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 20070124 10:34:13 