half-assed answer

So, I am taking Discrete Structure this summer, and I am currently on the pigeonhole principle.

One question from the exercise: Let d be a positive integer. Show that among any group of d + 1 integers (not necessarily consecutive) there are two with exactly the same remainder when divided by d.

My answer: There are d possible remainders. d + 1 integers imply that at least two integers will give the same remainder.

This is based on the proof that shows among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4--mainly that there are four possible remainders when dividing by 4.