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

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

10   for Tot=2 to 999
20     for X=1 to int(Tot/2)
30      Y=Tot-X
40      Lhs=X*Y
50      Rhs=160+90*gcd(X,Y)
60      if Lhs=Rhs then print X,Y,Lhs
70     next
80   next

finds

x       y      prod
10      34      340
2       125     250
2       170     340
1       250     250

Posted by Charlie on 2013-10-04 11:48:37