Determine all possible pairs (x,y) of positive integers, with x ≤ y, that satisfy this equation:

           x*y = 160 + 90*gcd(x,y)

I found the same solutions as Daniel, but it's necessary to check the self-consistency of the gcd.  (10,25) and (5,50) don't work because they have gcd 5 rather than 1.

Posted by Tristan on 2013-10-03 22:42:14