Two positive integer with prime number Let $a, b$ be distinct positive integers. Prove that there exists a prime $p$ such that when dividing both $a$ and $b$ by $p$, the remainder of $a$ is less than the remainder of $b$.

How can i solve this?
Just pick $p$ such that $a&lt;b&lt;p$
Just take a prime dividing $a$ but not $b$.