Luca, F.; Ward, T. An elliptic sequence is not a sampled linear recurrence sequence. (English) Zbl 1367.11020 New York J. Math. 22, 1319-1338 (2016). Summary: Let \(E\) be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let \(P = (x_1/z^2_1, y_1/z^3_1)\) 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 \((z_n)_{n\geqslant 1}\) defined by \(nP = (x_n/z^2_n, y_n/z^3_n)\) for all \(n > 1\) does not eventually coincide with \((u_{n^2})_{n>1}\) for any choice of linear recurrence sequence \((u_n)_{n\geqslant 1}\) with integer values. Cited in 1 Document MSC: 11B37 Recurrences 11G05 Elliptic curves over global fields Keywords:elliptic divisibility sequence; nontorsion point; linear recurrence sequence PDFBibTeX XMLCite \textit{F. Luca} and \textit{T. Ward}, New York J. Math. 22, 1319--1338 (2016; Zbl 1367.11020) Full Text: arXiv EMIS