Each of X and Y is a positive integer with X ≤ Y. The quotient and the remainder obtained upon dividing X² + Y² by X+Y are respectively denoted by Q and R.

Determine all possible pairs (X, Y) such that Q² + R = 1977

Supplementary questions:

This problem has been out of circulation for quite some time. Why? When is it likely to come back into favour?

   10   for X=1 to 2700
   20   for Y=X to 20000
   30    N=X*X+Y*Y:D=X+Y
   40    Q=N\D:R=N @ D
   50    if Q*Q+R=1977 then print X;Y,N;D,Q;R
   60   next
   70   next

 x   y            num  den        q   r 
 7   50          2549  57        44  41
 37  50          3869  87        44  41

 

Posted by Charlie on 2011-02-08 22:24:14