The greatest common divisor of linear recurrences
E Tron - Rendiconti del Seminario Matematico, 2020 - hal.science
The greatest common divisor of linear recurrences Page 1 HAL Id: hal-03129393 https://hal.science/hal-03129393
Submitted on 2 Feb 2021 HAL is a multi-disciplinary open access archive for the deposit …
Submitted on 2 Feb 2021 HAL is a multi-disciplinary open access archive for the deposit …
The distribution of GCDs of shifted primes and Lucas sequences
A Jha, A Nath - arXiv preprint arXiv:2207.00825, 2022 - arxiv.org
Let $(u_n) _ {n\ge 0} $ be a nondegenerate Lucas sequence and $ g_u (n) $ be the
arithmetic function defined by $\gcd (n, u_n). $ Recent studies have investigated the …
arithmetic function defined by $\gcd (n, u_n). $ Recent studies have investigated the …
On terms in a dynamical divisibility sequence having a fixed GCD with their indices
A Jha - arXiv preprint arXiv:2105.06190, 2021 - arxiv.org
Let $ F $ and $ G $ be integer polynomials where $ F $ has degree at least $2 $. Define the
sequence $(a_n) $ by $ a_n= F (a_ {n-1}) $ for all $ n\ge 1$ and $ a_0= 0. $ Let $\mathscr …
sequence $(a_n) $ by $ a_n= F (a_ {n-1}) $ for all $ n\ge 1$ and $ a_0= 0. $ Let $\mathscr …
Central binomial coefficients divisible by or coprime to their indices
C Sanna - International Journal of Number Theory, 2018 - World Scientific
Let 𝒜 be the set of all positive integers n such that n divides the central binomial coefficient 2
nn. Pomerance proved that the upper density of 𝒜 is at most 1− log 2. We improve this …
nn. Pomerance proved that the upper density of 𝒜 is at most 1− log 2. We improve this …
Greatest common divisors of shifted primes and Fibonacci numbers
Let (F n) be the sequence of Fibonacci numbers and, for each positive integer k, let P k be
the set of primes p such that gcd (p-1, F p-1)= k. We prove that the relative density r (P k) of P …
the set of primes p such that gcd (p-1, F p-1)= k. We prove that the relative density r (P k) of P …
[HTML][HTML] The moments of the logarithm of a GCD related to Lucas sequences
C Sanna - Journal of Number Theory, 2018 - Elsevier
Let (un) n≥ 0 be a nondegenerate Lucas sequence satisfying un= a 1 un− 1+ a 2 un− 2 for
all integers n≥ 2, where a 1 and a 2 are some fixed relatively prime integers; and let gu be …
all integers n≥ 2, where a 1 and a 2 are some fixed relatively prime integers; and let gu be …
[PDF][PDF] Index Divisibility in the Orbit of 0 for Integral Polynomials.
TA Gassert, MT Urbanski - Integers: Electronic Journal of …, 2020 - math.colgate.edu
#A16 INTEGERS 20 (2020) INDEX DIVISIBILITY IN THE ORBIT OF 0 FOR INTEGRAL
POLYNOMIALS T. Alden Gassert Department of Mathematics Page 1 #A16 INTEGERS 20 (2020) …
POLYNOMIALS T. Alden Gassert Department of Mathematics Page 1 #A16 INTEGERS 20 (2020) …
On the Galois Groups of Some Recursive Polynomials
K Monsef-Shokri - Bulletin of the Iranian Mathematical Society, 2022 - Springer
We show that for some recursive sequence ( c m ) m ≥ 1 \documentclass[12pt]{minimal} \usepackage{amsmath}
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\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} …
Index divisibility in the orbit of 0 for integral polynomials
TA Gassert, MT Urbanski - arXiv preprint arXiv:1709.08751, 2017 - arxiv.org
Let $ f (x)\in\bbz [x] $ and consider the index divisibility set $ D=\{n\in\bbn: n\mid f^ n (0)\} $.
We present a number of properties of $ D $ in the case that $(f^ n (0)) _ {n= 1}^\infty $ is a …
We present a number of properties of $ D $ in the case that $(f^ n (0)) _ {n= 1}^\infty $ is a …
[PDF][PDF] ARITHMETIC PROPERTIES OF LINEAR RECURRENCES AND OTHER TOPICS IN NUMBER THEORY
C Sanna - 2018 - iris.unito.it
This thesis is a recollection of several contributions to Number Theory. It is divided into two
parts, which are essentially independent from each other. In the first part, we prove a number …
parts, which are essentially independent from each other. In the first part, we prove a number …