Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.6

An Elementary Proof that any Natural Number can be Written as the Sum of Three Terms of the Sequence ⌊n2/3 ⌋

Bakir Farhi
Department of Mathematics
University of Béjaia


We give an elementary proof that any natural number can be written as the sum of three terms of the sequence ⌊ n2/3 ⌋nN . This is a recent conjecture of the author that was very recently confirmed by Mezroui et al.; they used a result due to Bateman and derived from the theory of modular forms. We also state some conjectures related to the subject.

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Received November 16 2013; revised versions received May 14 2014; May 29 2014; June 25 2014. Published in Journal of Integer Sequences, July 11 2014.

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