Towards Bauer's theorem for linear recurrence sequences

Mariusz Skałba. "Towards Bauer's theorem for linear recurrence sequences." Colloquium Mathematicae 98.2 (2003): 163-169. <http://eudml.org/doc/284925>.

@article{MariuszSkałba2003,
abstract = {Consider a recurrence sequence $(x_\{k\})_\{k∈ℤ\}$ of integers satisfying $x_\{k+n\} = a_\{n-1\}x_\{k+n-1\} + ... + a₁x_\{k+1\} + a₀x_\{k\}$, where $a₀,a₁,...,a_\{n-1\} ∈ ℤ$ are fixed and a₀ ∈ -1,1. Assume that $x_\{k\} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_\{k₀\} < 0$ then for each negative integer -D there exist infinitely many rational primes q such that $q|x_\{k\}$ for some k ∈ ℕ and (-D/q) = -1.},
author = {Mariusz Skałba},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {163-169},
title = {Towards Bauer's theorem for linear recurrence sequences},
url = {http://eudml.org/doc/284925},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Mariusz Skałba
TI - Towards Bauer's theorem for linear recurrence sequences
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 2
SP - 163
EP - 169
AB - Consider a recurrence sequence $(x_{k})_{k∈ℤ}$ of integers satisfying $x_{k+n} = a_{n-1}x_{k+n-1} + ... + a₁x_{k+1} + a₀x_{k}$, where $a₀,a₁,...,a_{n-1} ∈ ℤ$ are fixed and a₀ ∈ -1,1. Assume that $x_{k} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_{k₀} < 0$ then for each negative integer -D there exist infinitely many rational primes q such that $q|x_{k}$ for some k ∈ ℕ and (-D/q) = -1.
LA - eng
UR - http://eudml.org/doc/284925
ER -