Thread: Prime factor problem

Prove that each integer of the form 3n+2 has a prime factor of this form.

proof. Let a = 3n+2, suppose that p | a, p prime, then px = 3n + 2

Then I'm stuck, or should I write p = 3q + r?

Originally Posted by tttcomrader

Prove that each integer of the form 3n+2 has a prime factor of this form.

proof. Let a = 3n+2, suppose that p | a, p prime, then px = 3n + 2

Then I'm stuck, or should I write p = 3q + r?

Assume not. Then its prime factors p1,...,pn all have the form 3k+1. But then p1*p2*...*pn has the form 3k+1 also which is a contradiction.