Geodesic
Representation of integers using \(a^2 + b^2 - dc^2\)
Journal of integer sequences, Tome 18 (2015) no. 8
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},
     year = {2015},
     volume = {18},
     number = {8},
     zbl = {1332.11038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a4/}
}
TY  - JOUR
AU  - Lam,  Peter Cho-Ho
TI  - Representation of integers using \(a^2 + b^2 - dc^2\)
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a4/
LA  - en
ID  - JIS_2015__18_8_a4
ER  - 
%0 Journal Article
%A Lam,  Peter Cho-Ho
%T Representation of integers using \(a^2 + b^2 - dc^2\)
%J Journal of integer sequences
%D 2015
%V 18
%N 8
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a4/
%G en
%F JIS_2015__18_8_a4
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/