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Near Pythagoras (Posted on 2013-07-31) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: computer solution | Comment 2 of 4 |
(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

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