Geodesic
Common terms in binary recurrences
Communications in Mathematics, Tome 14 (2006) no. 1, pp. 57-61

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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 $c^2-(D+p)d^2=1$.
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 $c^2-(D+p)d^2=1$.
Classification : 11B37, 11B39, 11D09, 95U50
Keywords: Pell equation; binary sequences 
Orosz, Erzsébet. Common terms in binary recurrences. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 57-61. http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a8/
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