Journal of Integer Sequences, Vol. 17 (2014), Article 14.1.8

On a Conjecture of Farhi

Soufiane Mezroui, Abdelmalek Azizi, and M'hammed Ziane
Laboratoire ACSA
Département de Mathématiques et Informatique
Université Mohammed Premier
Oujda 60000


Recently, Farhi showed that every natural number N ≢ 2 (mod 24) can be written as the sum of three numbers of the form floor(n2/3) (nN). He conjectured that this result remains true even if N ≡ 2 (mod 24). In this note, we prove this statement.

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Received July 25 2013; revised versions received July 31 2013; November 22 2013; December 30 2013. Published in Journal of Integer Sequences, December 30 2013. Revision, January 3 2014.

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