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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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Analytical note | Comment 3 of 4 |
Let x = a + 1/2, where a is any integer.

then [x2] = [(a+1/2)^2] = [a^2+a+1/4] = a^2+a

So we need to find (a,b) such that a^2+a + b^2 + b = 2016

  Posted by Steve Herman on 2013-08-01 08:50:26
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