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 computer solution by Charlie)

Charlie:

WolframAlpha: floor[((2a-1)/2)^2] + floor[((2b-1)/2)^2]=2016, x=2a-1, y=2b-1 gives {x,y} = {±85,±29}{±71,±55}{±55,±71}{±29,±85} for a total of 16 solutions.

 

Edited on August 1, 2013, 3:14 am

Posted by broll on 2013-08-01 03:11:55