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
Morocco
Abstract:
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)
(n ∈ N).
He
conjectured that this result remains true even if N ≡ 2 (mod 24). In
this note, we prove this statement.
Full version: pdf,
dvi,
ps,
latex
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.
Return to
Journal of Integer Sequences home page
