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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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 One Set | Comment 1 of 7
I have the set (7,50).
This yields:
X² +Y²  =  2549   and X + Y = 57

The quotient Q²  (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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