Each of X and Y is a positive integer with X ≤ Y. The quotient and the remainder obtained upon dividing X^{2} + Y^{2} by X+Y are respectively denoted by Q and R.
Determine all possible pairs (X, Y) such that Q^{2} + 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?