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Number Theory problem: Fault in logic?
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I have this problem I got wrong:
If a and b are Coprime, show a b and a*b are Coprime.
Proof: Since a and b are Coprime, then a b and a are coprime as well as a b and b are Coprime.
Thus, a b and ab are Coprime. (QED)
I got it completely wrong apparently, and I looked up the proof involving squaring the unique integer solution. But that method doesn't seem as obvious as this, if it's right.
So, is my logic here correct, or are there potential counter examples?
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