The rank of apparition of powers of Lucas sequence

Authors : Prasanta Kumar RAY, Nurettin IRMAK, Bijan Kumar PATEL

Pages : 1566-1570

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Publication Date : 0000-00-00

Article Type : Research Paper

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