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Q^2 + R = 1977 (Posted on 2011-02-08) Difficulty: 3 of 5
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    
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One Set | Comment 1 of 7
I have the set (7,50).
This yields:
 X +Y  =  2549   and X + Y = 57

The quotient Q  (1936) + R (41) = 1977.

Variances within X and Y cause shifts around that value,
eg  X=  9 and Y = 51  yields  1978
     X =15 and Y = 53  yields  1978.
                                                   It would therefore seem that no other values fit that scenario.


For the Supplementary question I'm assuming that we are to look for the next year AD where a unique pairing only will yield that year.


  Posted by brianjn on 2011-02-08 22:07:54
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