On a conjecture on the representation of positive integers as the sum of three terms of the sequence \(\lfloor \frac{n^2}{a} \rfloor\)
Journal of integer sequences, Tome 18 (2015) no. 6
We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence $\lfloor n^{2}/a \rfloor $. This is done by generalizing a method used by Farhi in his original paper.
Classification : 11B13
Keywords: additive base, Legendre's theorem
@article{JIS_2015__18_6_a5,
     author = {Holdum,  Sebastian Tim and Klausen,  Frederik Ravn and Rasmussen,  Peter Michael Reichstein},
     title = {On a conjecture on the representation of positive integers as the sum of three terms of the sequence \(\lfloor \frac{n^2}{a} \rfloor\)},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {6},
     zbl = {1332.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a5/}
}
TY  - JOUR
AU  - Holdum,  Sebastian Tim
AU  - Klausen,  Frederik Ravn
AU  - Rasmussen,  Peter Michael Reichstein
TI  - On a conjecture on the representation of positive integers as the sum of three terms of the sequence \(\lfloor \frac{n^2}{a} \rfloor\)
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a5/
LA  - en
ID  - JIS_2015__18_6_a5
ER  - 
%0 Journal Article
%A Holdum,  Sebastian Tim
%A Klausen,  Frederik Ravn
%A Rasmussen,  Peter Michael Reichstein
%T On a conjecture on the representation of positive integers as the sum of three terms of the sequence \(\lfloor \frac{n^2}{a} \rfloor\)
%J Journal of integer sequences
%D 2015
%V 18
%N 6
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a5/
%G en
%F JIS_2015__18_6_a5
Holdum,  Sebastian Tim; Klausen,  Frederik Ravn; Rasmussen,  Peter Michael Reichstein. On a conjecture on the representation of positive integers as the sum of three terms of the sequence \(\lfloor \frac{n^2}{a} \rfloor\). Journal of integer sequences, Tome 18 (2015) no. 6. http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a5/