Geodesic
On a conjecture of Farhi
Journal of integer sequences, Tome 17 (2014) no. 1
Recently, Farhi showed that every natural number $N$ ≢ 2 (mod 24) can be written as the sum of three numbers of the form $floor(n^{2}/3) (n \in $ N). He conjectured that this result remains true even if $N \equiv 2$ (mod 24). In this note, we prove this statement.
Classification : 11B13
Keywords: additive base, Legendre's theorem, representation of an integer as the sum of three squares 
@article{JIS_2014__17_1_a2,
     author = {Mezroui,  Soufiane and Azizi,  Abdelmalek and Ziane,  M'hammed},
     title = {On a conjecture of {Farhi}},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {1},
     zbl = {1317.11019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a2/}
}
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Mezroui,  Soufiane; Azizi,  Abdelmalek; Ziane,  M'hammed. On a conjecture of Farhi. Journal of integer sequences, Tome 17 (2014) no. 1. http://geodesic.mathdoc.fr/item/JIS_2014__17_1_a2/