On the powerful part of n 2 + 1

Jan-Christoph Puchta

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 3, page 187-189
  • ISSN: 0044-8753

Abstract

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We show that n 2 + 1 is powerfull for O ( x 2 / 5 + ϵ ) integers n ≤ x at most, thus answering a question of P. Ribenboim.

How to cite

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Puchta, Jan-Christoph. "On the powerful part of $n^2+1$." Archivum Mathematicum 039.3 (2003): 187-189. <http://eudml.org/doc/249134>.

@article{Puchta2003,
abstract = {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.},
author = {Puchta, Jan-Christoph},
journal = {Archivum Mathematicum},
keywords = {powerfull integer},
language = {eng},
number = {3},
pages = {187-189},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the powerful part of $n^2+1$},
url = {http://eudml.org/doc/249134},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Puchta, Jan-Christoph
TI - On the powerful part of $n^2+1$
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 3
SP - 187
EP - 189
AB - 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.
LA - eng
KW - powerfull integer
UR - http://eudml.org/doc/249134
ER -

References

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  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. (1986) MR0848850
  2. Heath-Brown D. R., Review 651.10012, Zentralblatt Mathematik 651, 41 (1989) (1989) MR1441325
  3. Mardjanichvili C., Estimation d’une somme arithmetique, Dokl. Acad. Sci. SSSR 22 (1939), 387–389. (1939) Zbl0021.20802
  4. Ribenboim P., Remarks on exponential congruences and powerful numbers, J. Number Theory 29 (1988), 251–263. (1988) Zbl0651.10012MR0955951

NotesEmbed ?

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