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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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 $b$.
📌 3 Key Takeaways
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Objective & Hypothesis: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 $b$.
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Key Findings & Data: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 $b$.
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Conclusion & Impact: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 $b$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lucas sequence · periodicity · rank of apparition
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 $b$.
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Cite This Article
RAY, P. K., IRMAK, N., PATEL, B. K. (2022). The rank of apparition of powers of Lucas sequence. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 4, 1566–1570. https://ajindex.com/articles/607889