1. The problem statement, all variables and given/known data Prove if m/n has a repeating decimal expansion of period k, and n has no repeated prime factors, then some prime factor of n divides 10k-1 and no number of the form 10j-1 for 1 ≤ j < k 2. Relevant equations 3. The attempt at a solution I know that if a decimal expansion d has period 5, then d(10N+5-10N) is an integer for some number N representing the number of decimal places before the repeating part of the decimal expansion begins. I'm really not sure where to go with this problem though. I think it would simplify the problem if I knew the repeating portion of m/n began immediately after the decimal point. But I'm not sure how to prove that either.