Hint: From $x\equiv a\pmod n$, there is $q\in\mathbb Z$ with $x-a=nq$. Consider the two cases q even and q odd.
Prove the following conditional; If then either or
So just fiddling with x's and a's...
These all look like good conditionals to me so I'm satisfied that I can write a proof.
I've tried a direct proof where I just multiply by 2 but that doesn't seem too profitable.
My other idea is to assume that but that doesn't seem to work out well either.
Neither of which seem too promising.
Any ideas or errors?
Since q is either even or odd,
OK that looks great thanks!