Prove that if $a \in \mathbb Z$ then the only positive divisor of both $a$ and $a + 1$ is $1$.
When I saw this statement I didn't understand it. The only way that I can see it being true is if a is a negative number but since a ∈ Z a could also be positive and thus it could have more than one positive divisor. If that's the case would I have to disprove this instead of proving? And what would be the best way to do that?