Show that if a and b are integers with (a, b) : l, then (a*b, a-b) : i or 2.
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Answer:
From here I tried to proceed with two cases.
1: a−b is even, which leads to gcd(a+b,a−b)=2
2: a−b is odd, which leads to gcd(a+b,a−b)=1
My main problem I think is, that I do not know how I should include gcd(a,b)=1 in the proof.
Any help is appreciated. Thx in advance.
Cherio Woltan