Prove: If gcd(a,b) = 1, and c divides (a+b), then gcd(a,c) = gcd(b,c) = 1.

Help Please!

Let d = gcd(a,c). Then d divides a and d divides c. Since c divides a + b, d divides a + b. Since d divides a and d divides a + b, d divides (a + b) - a = b. Since d divides both a and b, d divides gcd(a,b) = 1. So d = 1. By a similar argument, gcd(b,c) = 1.