Primitive prime factors in second-order linear recurrence sequences

Andrew Granville

Type: Article

Publication Date: 2012-01-01

Citations: 2

DOI: https://doi.org/10.4064/aa155-4-7

Abstract

For a class of Lucas sequences {xn}, we show that if n is a positive integer then xn has a primitive prime factor which divides xn to an odd power, except perhaps when n = 1, 2, 3 or 6. This has several desirable consequences.

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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Works Cited by This (6)

Action	Title	Year	Authors
+	Primitive divisors of the expression An - Bn in algebraic number fields.	1974	Andrzej Schinzel
+ PDF Chat	On primitive prime factors of Lehmer numbers I	1963	Andrzej Schinzel
+ PDF Chat	Existence of primitive divisors of Lucas and Lehmer numbers	2001	Yonatan Bilu Guillaume Hanrot Paul Voutier
+ PDF Chat	On the Diophantine Equation <i>n</i>(<i>n</i> + <i>d</i>) · · · (<i>n</i> + (<i>k</i> − 1)<i>d</i>) = <i>by</i><sup><i>l</i></sup>	2004	Kálmán Győry Lajos Hajdu N. Saradha
+	Problems on Fibonacci Numbers and Their Generalizations	1986	A. Rotkiewicz
+	The Little Book of Bigger Primes	2004	Paulo Ribenboim