Thread: primes

Let n>1. If (n^2)+2 is a prime show that 3 divides n.

Can anyone help me start this exercise? Thank you

Originally Posted by AlexHall

Let n>1. If (n^2)+2 is a prime show that 3 divides n.

Try proving the contrapositive. If 3 does not divide n then n must be of the form 3k+1 or 3k+2. Show that in both cases (n^2)+2 is then a multiple of 3.