 

F. Luca and T. Ward
An elliptic sequence is not a sampled linear recurrence sequence view print


Published: 
November 8, 2016

Keywords: 
Elliptic divisibility sequence; nontorsion point; linear recurrence sequence 
Subject: 
11B37; 11G05 


Abstract
Let E be an elliptic curve defined over the rationals
and in minimal Weierstrass form, and let P=(x_{1}/z_{1}^{2},y_{1}/z_{1}^{3})
be a rational point of infinite order on E, where x_{1},y_{1},z_{1}
are coprime integers. We show that the integer
sequence (z_{n})_{n≧1} defined by nP=(x_{n}/z_{n}^{2},y_{n}/z_{n}^{3}) for all n≧ 1
does not eventually coincide with (u_{n2})_{n≧1}
for any choice of linear recurrence sequence (u_{n})_{n≧1} with integer values.


Author information
F. Luca:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Florian.Luca@wits.ac.za
T. Ward:
Ziff Building, University of Leeds, Leeds LS2 9JT, UK
t.b.ward@leeds.ac.uk

