2n^2=m^2
Why is 2 a factor of m?
So, m and n are integers.
If m^2 is twice n^2 that means m^2 is even. (Which is the same as saying 2 is a factor of m^2.) But if m^2 is even then m must also be even.
As it turns out, we know something stronger: that 4 is a factor of m.
Are you looking at a proof that the square root of 2 is irrational, by chance?