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Floor Sum Formulation (Posted on 2014-10-05)

Determine all possible pairs (x, y) of positive integers satisfying:
floor(x²/y) + floor(y²/x) = floor(x/y + y/x)+ x*y.

Prove that there are no others.

No Solution Yet Submitted by K Sengupta

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There are infinite number of solutions.

They are of the form (n, n^2 + 1)

(1,2), (2,5), (3,10), (4,17), (5,26), (6,37), (7,50), (8,65), (9,82), ....

Posted by Benny on 2014-10-05 17:42:18

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