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
Béjaia
Algeria
Abstract:
We give an elementary proof that any natural number can be written as
the sum of three terms of the
sequence ⌊ n2/3 ⌋n ∈ N .
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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