The rank of apparition of powers of Lucas sequence

Authors

PRASANTA KUMAR RAY
NURETTİN IRMAK
BIJAN KUMAR PATEL

DOI

10.3906/mat-1705-116

Abstract

This note is devoted to studying the divisibility relation $u_{n}^{k+1} u_{m}$ for a least positive integer $m$, where $\{u_{n}\}_{n \geq 0}$ is a nondegenerate Lucas sequence with characteristic polynomial $x^{2}-ax - b,$ for some relatively prime integers $a$ and $b$.

Keywords

Lucas sequence, periodicity, rank of apparition, $p$-adic order

First Page

1566

Last Page

1570

Recommended Citation

RAY, PRASANTA KUMAR; IRMAK, NURETTİN; and PATEL, BIJAN KUMAR (2018) "The rank of apparition of powers of Lucas sequence," Turkish Journal of Mathematics: Vol. 42: No. 4, Article 3. https://doi.org/10.3906/mat-1705-116
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/3