Prime divisors of some shifted products

Eric Levieil; Florian Luca; Igor E. Shparlinski

doi:10.1155/IJMMS.2005.3057

Prime divisors of some shifted products

Eric Levieil, Florian Luca, Igor E. Shparlinski

School of Computing

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Abstract

We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that the ratios a(n) = A(n)/A(n - 1) have some number-theoretic or combinatorial meaning. In the case a(n) = n, we obviously have A (n) = n!, for which several new results about prime divisors of n! + 1 have recently been obtained.

Original language	English
Pages (from-to)	3057-3073
Number of pages	17
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2005
Issue number	19
DOIs	https://doi.org/10.1155/IJMMS.2005.3057
Publication status	Published - 2005

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title = "Prime divisors of some shifted products",

abstract = "We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that the ratios a(n) = A(n)/A(n - 1) have some number-theoretic or combinatorial meaning. In the case a(n) = n, we obviously have A (n) = n!, for which several new results about prime divisors of n! + 1 have recently been obtained.",

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

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AU - Luca, Florian

AU - Shparlinski, Igor E.

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Y1 - 2005

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AB - We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that the ratios a(n) = A(n)/A(n - 1) have some number-theoretic or combinatorial meaning. In the case a(n) = n, we obviously have A (n) = n!, for which several new results about prime divisors of n! + 1 have recently been obtained.

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 19

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Prime divisors of some shifted products

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