I read this somewhere recently.
For any natural number n, there exists a multiple of n, such that the multiple has only 0 and 1 as it's digits.
For e.g for 2, 3, 4, 5, 6 etc we have 10, 111, 100, 10, 1110 etc
Any ideas how to go about proving this?
Problem 303 - Project Euler
then in the solution forum you will find some nice related discussion. Unfortunately I don't have time to adapt everything to this problem and then hide the source so people can't cheat.
Problem 303 is pretty easy, but could be hard if you're not already familiar with a programming language.