Geodesic
The numbers \(a^2 + b^2 - dc^2\)
Journal of integer sequences, Tome 18 (2015) no. 2
We say that a positive integer $d$ is special if for every integer $m$ there exist nonzero integers $a, b, c$ such that $m = a^{2} + b^{2} - dc^{2}$. In this note we present examples and some properties of special numbers. Moreover, we present an infinite sequence of special numbers.
Classification : 11D09, 11B99
Keywords: pell's equation, sum of squares 
@article{JIS_2015__18_2_a0,
     author = {Nowicki,  Andrzej},
     title = {The numbers \(a^2 + b^2 - dc^2\)},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {2},
     zbl = {1310.11035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_2_a0/}
}
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Nowicki,  Andrzej. The numbers \(a^2 + b^2 - dc^2\). Journal of integer sequences, Tome 18 (2015) no. 2. http://geodesic.mathdoc.fr/item/JIS_2015__18_2_a0/