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?
(In reply to
re: Supplementary questions by Charlie)
As usual, Charlie, I'm probably wrong, but 44 + 41/44 is less than 45, so that Q^2=1936. 1936+41=1977. Then taking your example, 44+74/44 is 45+30/74, and Q^2 is 2025. Your 'remainder' is larger than 1, so increases the quotient by 1.
If remainders that were improper fractions were allowed, there would be no reason not to use 2010 in place of 1977, as you rightly point out.

Posted by broll
on 20110209 15:56:25 