A Trivial Note Concerning p and n!, where p is Prime ≥ n + 1 and n is an Integer ≥ 1

We show that if n is an integer 1 and if p is a prime n + 1, then for every integer ksuch that 1 k n, p does not divide k!; where k! = 1 :::: k; in particular, if p is a prime n + 1,then the greatest common divisor of p and n! is 1 and therefore p does not divide n!