Question

let n be a positive integer and p e a prime. prove: p|n! if and only if p<= n

Answer 1

sorry, I think my argue is strong but it's not.

Answer 2

It's actually pretty obvious.\[n! = n(n - 1)(n - 2)(n - 3)\cdots 1\]All integers \(\le n\) divide \(n!\), where \(p\) is included. However, because \(n!\) and \(p\) are coprime when \(p> n!\), we may say \(p \not{|} ~n!\)

Answer 3

ok thanks