It is standard result about primes that if p is prime then w

It is standard result about primes that if p is prime, then whenever p divides a product ab, p divides at least one a, b. Prove the converse, that any natural number having this property (for any pair a, b) must be prime.

Solution

Suppose p is not prime having thsi property that p divides at least a or b

a and b are any two numbers

ab=pk k belongs to Z

=> p divides ab

by assumption p divides a or b , contradiction to p is not prime