Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.3

On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋


Sebastian Tim Holdum
Niels Bohr Institute
University of Copenhagen
Denmark

Frederik Ravn Klausen and Peter Michael Reichstein Rasmussen
Department of Mathematics
University of Copenhagen
Denmark

Abstract:

We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence ⌊ n2/a ⌋. This is done by generalizing a method used by Farhi in his original paper.

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Received September 29 2014; revised version received March 5 2015; May 19 2015. Published in Journal of Integer Sequences, May 31 2015.

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