Question

Prove that 3 divides 2n^2 + 1 if and only if 3 does not divide n

Answer 1

let's do the first of two cases we need to show
3|(2n^2+1)=>3 does not divide n
We can try a proof by contradiction if you want
That is maybe you can suppose 3|(2n^2+1) and 3|n
and arrive at some contradiction

Answer 2

use mathway.com