Math 311W Problem Set 4 Due Friday, September 25, 2015 1. Let a, b, c Z with a = 0. Prove that if a | b and a | c, then a | (bm + cn) for any n, m Z. 2. Let n Z with n > 0. Prove that n | (n + 1)2015 1 . 3. Let n Z. Prove that 3 | (n3 n). 4. Find gcd(a, b) and express the gcd in the form ax + by. (a) a = 361, b = 1178. (b) a = 525, b = 231. 1