Suppose b,c∈Z+ are relatively prime (i.e., gcd), and a \,|\, (b+c). Prove that \gcd(a,b) = 1 and \gcd(a,c) = 1.
I've been trying to brainstorm how to prove this. I have determined that \gcd(b, b + c) = 1, but I am not sure if this fact will aid in proving this statement at all.
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