Geodesic
An elementary proof that any natural number can be written as the sum of three terms of the sequence \(\lfloor \frac{n}{2/3} \rfloor \)
Journal of integer sequences, Tome 17 (2014) no. 7
Zbl
We give an elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor n^{2}/3 \rfloor _{n \in N}$ . This is a recent conjecture of the author that was very recently confirmed by Mezroui et al.; they used a result due to Bateman and derived from the theory of modular forms. We also state some conjectures related to the subject.
Keywords: sum of squares, Legendre's theorem, additive bases 
Farhi,  Bakir. An elementary proof that any natural number can be written as the sum of three terms of the sequence \(\lfloor \frac{n}{2/3} \rfloor \). Journal of integer sequences, Tome 17 (2014) no. 7. http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a1/
@article{JIS_2014__17_7_a1,
     author = {Farhi,  Bakir},
     title = {An elementary proof that any natural number can be written as the sum of three terms of the sequence \(\lfloor \frac{n}{2/3} \rfloor \)},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {7},
     zbl = {1317.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_7_a1/}
}
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