Math 311W Problem Set 6 Due Friday, October 23, 2015 1. Let a, b Z such that a b mod n. If m is a positive integer such that m | n, then prove that a b mod m. 2. Let a, b Z such that a b (mod n). If c is a positive integer, then prove that ca cb mod cn. 3. Let a, b Z such that a b (mod n). If d is a positive integer such that d | a, d | b, d | n, then prove that a b d d mod n . d 4. Let a, b Z such that a b mod m. If n is a positive intger such that m | n, then prove that a b + mi mod n n for some i, i = 0, . . . , ( m 1). 5. Solve the following congruence. 66x 75 1 mod 105