On the powerful part of $n\sp 2+1$
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 187-189 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We show that $n^2+1$ is powerfull for $O(x^{2/5+\epsilon })$ integers $n\le x$ at most, thus answering a question of P. Ribenboim.
We show that $n^2+1$ is powerfull for $O(x^{2/5+\epsilon })$ integers $n\le x$ at most, thus answering a question of P. Ribenboim.
Classification : 11D09, 11D25, 11N25
@article{ARM_2003_39_3_a3,
     author = {Puchta, Jan-Christoph},
     title = {On the powerful part of $n\sp 2+1$},
     journal = {Archivum mathematicum},
     pages = {187--189},
     year = {2003},
     volume = {39},
     number = {3},
     mrnumber = {2010719},
     zbl = {1122.11311},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a3/}
}
TY  - JOUR
AU  - Puchta, Jan-Christoph
TI  - On the powerful part of $n\sp 2+1$
JO  - Archivum mathematicum
PY  - 2003
SP  - 187
EP  - 189
VL  - 39
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a3/
LA  - en
ID  - ARM_2003_39_3_a3
ER  - 
%0 Journal Article
%A Puchta, Jan-Christoph
%T On the powerful part of $n\sp 2+1$
%J Archivum mathematicum
%D 2003
%P 187-189
%V 39
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a3/
%G en
%F ARM_2003_39_3_a3
Puchta, Jan-Christoph. On the powerful part of $n\sp 2+1$. Archivum mathematicum, Tome 39 (2003) no. 3, pp. 187-189. http://geodesic.mathdoc.fr/item/ARM_2003_39_3_a3/

[1] Evertse J.-H., Silverman J. H.: Uniform bounds for the number of solutions to $Y^n=f(X)$. Math. Proc. Camb. Philos. Soc. 100 (1986), 237–248. | MR

[2] Heath-Brown D. R.: Review 651.10012. Zentralblatt Mathematik 651, 41 (1989) | MR

[3] Mardjanichvili C.: Estimation d’une somme arithmetique. Dokl. Acad. Sci. SSSR 22 (1939), 387–389. | Zbl

[4] Ribenboim P.: Remarks on exponential congruences and powerful numbers. J. Number Theory 29 (1988), 251–263. | MR | Zbl