Geodesic
Powerful values of quadratic polynomials
Journal of integer sequences, Tome 14 (2011) no. 3
We study the set of those integers $k$ such that $n^{2} + k$ is powerful for infinitely many positive integers $n$. We prove that most integers $k$ have this property.
Keywords: powerful numbers, generalized pell equation 
@article{JIS_2011__14_3_a1,
     author = {de Koninck,  Jean-Marie and Doyon,  Nicolas and Luca,  Florian},
     title = {Powerful values of quadratic polynomials},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {3},
     zbl = {1229.11003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a1/}
}
TY  - JOUR
AU  - de Koninck,  Jean-Marie
AU  - Doyon,  Nicolas
AU  - Luca,  Florian
TI  - Powerful values of quadratic polynomials
JO  - Journal of integer sequences
PY  - 2011
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a1/
LA  - en
ID  - JIS_2011__14_3_a1
ER  - 
%0 Journal Article
%A de Koninck,  Jean-Marie
%A Doyon,  Nicolas
%A Luca,  Florian
%T Powerful values of quadratic polynomials
%J Journal of integer sequences
%D 2011
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a1/
%G en
%F JIS_2011__14_3_a1
de Koninck,  Jean-Marie; Doyon,  Nicolas; Luca,  Florian. Powerful values of quadratic polynomials. Journal of integer sequences, Tome 14 (2011) no. 3. http://geodesic.mathdoc.fr/item/JIS_2011__14_3_a1/