perplexus.info :: Just Math : Near Pythagoras

Near Pythagoras (Posted on 2013-07-31)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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