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?
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 20110208 22:07:54 