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
Sums of S-units in recurrence sequences
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DOI: 10.1016/j.jnt.2018.10.009
Abstract: Abstract In this paper we give various finiteness results concerning terms of recurrence sequences U n representable as a sum of S-units with a fixed number of terms. We prove that under certain (necessary) conditions,… read more here.
Keywords: recurrence sequences; number; sums units; recurrence ... See more keywords
Linear combinations of prime powers in binary recurrence sequences
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DOI: 10.1142/s1793042117500166
Abstract: We give finiteness results concerning terms of linear recurrence sequences having a representation as a linear combination, with fixed coefficients, of powers of fixed primes. On one hand, under certain conditions, we give effective bounds… read more here.
Keywords: linear combinations; recurrence; recurrence sequences; combinations prime ... 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