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Near Pythagoras (
Posted on 20130731
)
Determine all possible pairs (x,y) of
halfintegers
, with x ≤ y, that satisfy this equation:
[x
^{2}
] + [y
^{2}
] = 2016
Prove that there are no others.
*** [x] denotes the greatest integer ≤ x.
No Solution Yet
Submitted by
K Sengupta
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Comments: (
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)
Analytical note
 Comment 3 of 4 
Let x = a + 1/2, where a is any integer.
then
[x
^{2}
] = [(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 20130801 08:50:26
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