| Title:
|
On the powerful part of $n\sp 2+1$ (English) |
| Author:
|
Puchta, Jan-Christoph |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
187-189 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| MSC:
|
11D09 |
| MSC:
|
11D25 |
| MSC:
|
11N25 |
| idZBL:
|
Zbl 1122.11311 |
| idMR:
|
MR2010719 |
| . |
| Date available:
|
2008-06-06T22:41:43Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107865 |
| . |
| Reference:
|
[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 0848850 |
| Reference:
|
[2] Heath-Brown D. R.: Review 651.10012.Zentralblatt Mathematik 651, 41 (1989) MR 1441325 |
| Reference:
|
[3] Mardjanichvili C.: Estimation d’une somme arithmetique.Dokl. Acad. Sci. SSSR 22 (1939), 387–389. Zbl 0021.20802 |
| Reference:
|
[4] Ribenboim P.: Remarks on exponential congruences and powerful numbers.J. Number Theory 29 (1988), 251–263. Zbl 0651.10012, MR 0955951 |
| . |
