In a question that required proof by exhaustion, there are cases where any two numbers would not be multiples of each other. I came up with this statement, but I have 0 idea how to prove this:
$(\forall x \in Z, b \neq xa \land a,b \mod2 = 1) \rightarrow (\forall u \in Z, \exists v \in Z, u|a| - v|b| = 1 \lor v|b| - u|a| = 1)$
I'm not completely sure if this proof is written correctly, but the idea is how if a and b are odd and are not multiples of each other, they can always be manipulated with coefficients to equal 1.
I'm also most likely required to do it for even, even equals 2, and odd, even equals 1.