On the p-Adic Valuation of Third Order Linear Recurrence Sequences
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DOI: 10.1007/s00025-024-02311-3
Abstract: In a recent paper, Bilu et al. studied a conjecture of Marques and Lengyel on the p-adic valuation of the Tribonacci sequence. In this article, we study the p-adic valuation of third order linear recurrence… read more here.
Keywords: order linear; linear recurrence; document; third order ... See more keywords
Decomposable polynomials in second order linear recurrence sequences
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DOI: 10.1007/s00229-018-1070-8
Abstract: We study elements of second order linear recurrence sequences $$(G_n)_{n= 0}^{\infty }$$(Gn)n=0∞ of polynomials in $${{\mathbb {C}}}[x]$$C[x] which are decomposable, i.e. representable as $$G_n=g\circ h$$Gn=g∘h for some $$g, h\in {{\mathbb {C}}}[x]$$g,h∈C[x] satisfying $$\deg g,\deg h>1$$degg,degh>1.… read more here.
Keywords: second order; order linear; recurrence sequences; linear recurrence ... See more keywords
Intervals without primes near elements of linear recurrence sequences
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DOI: 10.1142/s1793042118500355
Abstract: Let (fn)n=1∞ be an unbounded sequence of integers satisfying a linear recurrence relation with integer coefficients. We show that for any k ∈ ℕ there exist infinitely many n ∈ ℕ for which 2k +… read more here.
Keywords: recurrence; without primes; intervals without; near elements ... See more keywords
On the zero–multiplicity of a fifth-order linear recurrence
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DOI: 10.1142/s1793042119500301
Abstract: We consider a family of linear recurrence sequences [Formula: see text] of order [Formula: see text] whose first [Formula: see text] terms are [Formula: see text] and each term afterwards is the sum of the… read more here.
Keywords: zero multiplicity; see text; linear recurrence; formula see ... See more keywords
On the fourth-order linear recurrence formula related to classical Gauss sums
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DOI: 10.1515/math-2017-0104
Abstract: Abstract Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the… read more here.
Keywords: order linear; order; recurrence formula; fourth order ... See more keywords
p-Adic quotient sets: Linear recurrence sequences with reducible characteristic polynomials
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DOI: 10.4153/s0008439524000547
Abstract: Abstract Let $(x_n)_{n\geq 0}$ be a linear recurrence sequence of order $k\geq 2$ satisfying $$ \begin{align*}x_n=a_1x_{n-1}+a_2x_{n-2}+\dots+a_kx_{n-k}\end{align*} $$ for all integers $n\geq k$ , where $a_1,\dots ,a_k,x_0,\dots , x_{k-1}\in \mathbb {Z},$ with $a_k\neq 0$ . In… read more here.
Keywords: characteristic polynomials; linear recurrence; adic quotient; recurrence sequences ... See more keywords