(a) Let a, b, c with gcd(a, b) = 1 and c|a + b. Prove that gcd(a, c) = 1 = gcd(b, c).

(b) Let a, b, c with gcd(a, b) = gcd(a, c) = 1. Prove that gcd(a, bc) = 1.

Hint: For both of these problems it is helpful to know that for any two integers m and n, if there exists integers, k and t such that mk + nt = 1 then we can conclude that gcd(m, n) = 1. Make sure you understand this hint!