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

Department of Computing

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

1 Citation (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

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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).",

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

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