Question 41:

(a)Use Fermat's Little Theorem to show that, for every prime p other than 2 or 5, there is some positive integer r for which p|(10^r -1) .

(b)Is it true that, for all integers n, other than multiples of 2 and 5, there is some positive integer r for which n|(10^r -1) .

(c)What is the relationship between these questions and decimal expansions?