Geodesic
Representation of integers using $a^2 + b^2 - dc^2$
Journal of integer sequences, Tome 18 (2015) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A positive integer $d$ is called special if every integer $m$ can be expressed as $a^{2} + b^{2} - dc^{2}$ for some nonzero integers $a,b,c$. A necessary condition for special numbers was recently given by Nowicki, and in this paper we prove its sufficiency. Thus, we give a complete characterization for special numbers.
Classification : 11D09
Keywords: sum of squares, sum of two coprime squares 
@article{JIS_2015__18_8_a4,
     author = {Lam, Peter Cho-Ho},
     title = {Representation of integers using $a^2 + b^2 - dc^2$},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {18},
     number = {8},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a4/}
}
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Lam, Peter Cho-Ho. Representation of integers using $a^2 + b^2 - dc^2$. Journal of integer sequences, Tome 18 (2015) no. 8. http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a4/