TITLE: Prove that $x$ and $x+1$ are coprime numbers
QUESTION [11 upvotes]: Given $\{x \mid x > 1\}$, how do I prove that any given $x$ and $x+1$ are coprime?

REPLY [3 votes]: If $x$ is a multiple of $p$, then the next multiple of $p$ is $x+p$, but that's clearly larger than $x+1$.