Show that if a, b, and c are integers such that gcd(a,b) = 1 and c divides a + b, then gcd(c, a) = gcd(c, b) = 1.
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Step 1
We have three integers \(a\), \(b\), and \(c\) such that \(\gcd(a, b) = 1\) and \(c\) divides \(a + b\). We need to show that \(\gcd(c, a) = 1\) and \(\gcd(c, b) = 1\). Show more…
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