On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence $\left\lfloor \frac{n^2}{a} \right\rfloor$

Sebastian Tim Holdum; Frederik Ravn Klausen; Peter Michael Reichstein Rasmussen

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arXiv · 1507.00369

On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence $\left\lfloor \frac{n^2}{a} \right\rfloor$

Sebastian Tim Holdum·Frederik Ravn Klausen·Peter Michael Reichstein Rasmussen

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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 $ \left\lfloor\frac{n^2}{a}\right\rfloor$. This is done by generalizing a method used by Farhi in his original paper.

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Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen. 2015-06-18. On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence $\left\lfloor \frac{n^2}{a} \right\rfloor$. https://arxiv.org/abs/1507.00369

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