Towards Bauer's theorem for linear recurrence sequences

• Autorzy: Mariusz Skałba
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B37: Recurrences
• 11A41: Primes
• 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 98
• Numer: 2
• Strony: 163-169

Daty

wydano

2003

Twórcy

autor

Mariusz Skałba

• Department of Mathematics, Computer Science and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm98-2-3