Suppose b,c∈Z+ are relatively prime (i.e., gcd(b,c)=1), 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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