On the largest prime factor of n! + 2n − 1

Florian Luca; Igor E. Shparlinski

doi:10.5802/jtnb.524

On the largest prime factor of n! + 2ⁿ − 1

Florian Luca, Igor E. Shparlinski

School of Computing

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For an integer n ≥ 2 we denote by P(n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n! + 2ⁿ − 1 ≡ 0 (mod q) and use these bounds to show that (formula presented).

Original language	English
Pages (from-to)	859-870
Number of pages	12
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	17
Issue number	3
DOIs	https://doi.org/10.5802/jtnb.524
Publication status	Published - 2005

Access to Document

10.5802/jtnb.524

Cite this

@article{8a90d127799d47ce8b897fc0f3317d70,

title = "On the largest prime factor of n! + 2n − 1",

abstract = "For an integer n ≥ 2 we denote by P(n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n! + 2n − 1 ≡ 0 (mod q) and use these bounds to show that (formula presented).",

author = "Florian Luca and Shparlinski, {Igor E.}",

year = "2005",

doi = "10.5802/jtnb.524",

language = "English",

volume = "17",

pages = "859--870",

journal = "Journal de Theorie des Nombres de Bordeaux",

issn = "1246-7405",

publisher = "Societe Arithmetique de Bordeaux",

number = "3",

}

TY - JOUR

T1 - On the largest prime factor of n! + 2n − 1

AU - Luca, Florian

AU - Shparlinski, Igor E.

PY - 2005

Y1 - 2005

N2 - For an integer n ≥ 2 we denote by P(n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n! + 2n − 1 ≡ 0 (mod q) and use these bounds to show that (formula presented).

AB - For an integer n ≥ 2 we denote by P(n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n! + 2n − 1 ≡ 0 (mod q) and use these bounds to show that (formula presented).

UR - http://www.scopus.com/inward/record.url?scp=85010006591&partnerID=8YFLogxK

U2 - 10.5802/jtnb.524

DO - 10.5802/jtnb.524

M3 - Article

AN - SCOPUS:85010006591

SN - 1246-7405

VL - 17

SP - 859

EP - 870

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

IS - 3

ER -

On the largest prime factor of n! + 2ⁿ − 1

Abstract

Access to Document

Other files and links

Fingerprint

Cite this