I'm not sure this is how you are expected to solve this, or even if thisOriginally Posted by delpin
is the simplest method; but:
First divide through by and rearrange to get:
Now this gives:
So there exists an integer such that:
Now the LHS (left hand side) is even, so must be odd.
So let , then:
But the LHS is divisible by so the RHS must also be divisible by
so must be even., so we may write it as , and then:
Now substituting this back into gives:
So we see that for any :
is a solution.