# (a) If gcd(a, 35) = 1, show that a12 = 1 (mod 35).[Hint: From Fermat's theorem a6 = 1

**Chapter 5, Problem 2**

(choose chapter or problem)

(a) If gcd(a, 35) = 1, show that a12 = 1 (mod 35).[Hint: From Fermat's theorem a6 = 1 (mod 7) and a4 = 1 (mod 5).](b) If gcd(a, 42) = 1, show that 168 = 3 7 8 divides a6 - 1.(c) If gcd(a, 133) = gcd(b, 133) = 1, show that 1331 a18 - b18

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