



 
Hi Tomas. Let x = GCD (a + b, a  b). Then x  (a+b) and x  (ab), by definition. Thus, x  [(a+b) + (ab)] (if it goes into one and it goes into the other, it goes into the sum). But this reduces to x  2a. So either x  2, or x  a. But since a and b are relatively prime, we know that x cannot divide a unless x = 1. Thus x = 1 or 2. Hope this helps,  


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