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We prove some cases of a conjecture by Farhi on the representation of everypositive integer as the sum of three terms of the sequence $\left\lfloor\frac{n^2}{a}\right\rfloor$. This is done by generalizing a methodused by Farhi in his original paper.

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