Let gcd(10, n)=1 , and let r be the smallest positive integer for which 10^r congruent to 1 (modulo n)

(a)Prove that 1/n has a recurring decimal expansion with period r.

(b)If n is prime, prove that r|(n-1).

(c)Find the periods of 1/13, 1/17, 2/31, and 1/47.