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 Q^2 + R = 1977 (Posted on 2011-02-08)
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?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solutions | Comment 2 of 7 |
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

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