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?

I don't know the answers to these. It doesn't seem to be because of the year, as in requesting 2010, we have

x=31  y=53          numerator=3770  denominator=84        quotient =44  remainder=74

There isn't one for 2011, but for 2012 we have

 x=34  y=52          numerator=3860  denominator=86       quotient = 44  remainder=76

 

Posted by Charlie on 2011-02-08 22:32:00