Prove that given any $17$ integers, there exist nine of them whose sum is divisible by $9.$
I'm pretty sure we have to use the pigeonhole principle, with the possible remainders as the pigeonhole, but that gives a lot of possibilities and I don't know where to start.
I tried to compare it to this question which was easier to solve:
Prove that given any $5$ integers, there exist three of them whose sum is divisible by $3.$