Common terms in binary recurrences

Orosz, Erzsébet. "Common terms in binary recurrences." Acta Mathematica Universitatis Ostraviensis 14.1 (2006): 57-61. <http://eudml.org/doc/35163>.

@article{Orosz2006,
abstract = {The purpose of this paper is to prove that the common terms of linear recurrences $M(2a,-1,0,b)$ and $N(2c,-1,0,d)$ have at most $2$ common terms if $p=2$, and have at most three common terms if $p>2$ where $D$ and $p$ are fixed positive integers and $p$ is a prime, such that neither $D$ nor $D+p$ is perfect square, further $a,b,c,d$ are nonzero integers satisfying the equations $a^2-Db^2=1$ and $c^2-(D+p)d^2=1$.},
author = {Orosz, Erzsébet},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Pell equation; binary sequences; common terms; second-order linear recursive sequence},
language = {eng},
number = {1},
pages = {57-61},
publisher = {University of Ostrava},
title = {Common terms in binary recurrences},
url = {http://eudml.org/doc/35163},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Orosz, Erzsébet
TI - Common terms in binary recurrences
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2006
PB - University of Ostrava
VL - 14
IS - 1
SP - 57
EP - 61
AB - The purpose of this paper is to prove that the common terms of linear recurrences $M(2a,-1,0,b)$ and $N(2c,-1,0,d)$ have at most $2$ common terms if $p=2$, and have at most three common terms if $p>2$ where $D$ and $p$ are fixed positive integers and $p$ is a prime, such that neither $D$ nor $D+p$ is perfect square, further $a,b,c,d$ are nonzero integers satisfying the equations $a^2-Db^2=1$ and $c^2-(D+p)d^2=1$.
LA - eng
KW - Pell equation; binary sequences; common terms; second-order linear recursive sequence
UR - http://eudml.org/doc/35163
ER -