Determine all possible pairs (x,y) of half-integers, with x ≤ y, that satisfy this equation:

[x²] + [y²] = 2016

Prove that there are no others.

*** [x] denotes the greatest integer ≤ x.

(In reply to re: computer solution by broll)

Of the 16 WolframAlpha solutions, only half have x <= y. The only two that my list failed to include were two cases where both x and y were negative:

x=-85/2, y=-29/2

x=-71/2, y=-55/2

So there are actually 8 solutions.

Posted by Charlie on 2013-08-01 09:41:59