The problem states:
In every set of 100 integers, there exists two distinct integers x and y s.t. 89 | (x-y)
So far the only thing I've determined is that 89 is prime, so 89 | (x-y) if (x-y) = k*89 where k is an integer. I understand the statement, and I see how in every set of 100 integers, there will always exist an x and y s.t. (x-y) will be a multiple of 89, but how would I start formally proving this?
Any help would be appreciated.