Let n ? 2 be an integer.
? Let S be a set of n + 1 integers. Prove that S contains two elements whose di?erence is divisible by n.
Hint: Use the Pigeonhole Principle.
? Prove that there is an integer that is divisible by n and whose decimal representation only contains the digits 0 and 5
. Hint: Consider the integers 5, 55, 555, 5555, …