Just as the title says, Prove that any collection of $8$ distinct integers contains distinct $x$ and $y$ such that $x - y$ is divisible by $7$.
I have seen a couple of questions here that are almost identical to this question but all of the answer for them are very brief so I was not able to fully understand how to do this question. I have an answer key and it says the following:
Pigeonholes : $0,1,\dots, 6$ ( all possible remainders after division by $7$)
Pigeons : $8$ distinct integers
As you can tell it's quite brief for an answer key. I was wondering if someone could explain to me how to use Pigeonhole principle here to get the answer in a little more detail.