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GCD to product (Posted on 2013-10-03) Difficulty: 3 of 5
Determine all possible pairs (x,y) of positive integers, with x ≤ y, that satisfy this equation:
           x*y = 160 + 90*gcd(x,y)

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 4 of 4 |

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
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