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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 42 Issue: 3

Some New Identities Concerning Generalized Fibonacciand Lucas Numbers

Zafer Şiar
Refik Keskin
Pages
—
Publication Date
2013-03-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some of them are new and some are well known.By using some of these identities we give some congruences concerninggeneralized Fibonacci and Lucas numbers such asV 2mn+r ≡ (−(−t)m ) n V r (mod Vm ), U 2mn+r ≡ (− (−t)m ) n U r (mod Vm ), and V 2mn+r ≡ (−t)mn V r (mod Um ), U 2mn+r ≡ (−t)mn U r (mod Um ).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we obtain some identities containing generalized Fibonacciand Lucas numbers.
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Key Findings & Data:In this paper we obtain some identities containing generalized Fibonacciand Lucas numbers.
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Conclusion & Impact:Some of them are new and some are well known.By using some of these identities we give some congruences concerninggeneralized Fibonacci and Lucas numbers such asV 2mn+r ≡ (−(−t)m ) n V r (mod Vm ), U 2mn+r ≡ (− (−t)m ) n U r (mod Vm ), and V 2mn+r ≡ (−t)mn V r (mod Um ), U 2mn+r ≡ (−t)mn U r (mod Um ).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized Fibonacci numbers · Generalized Lucas numbers · 2000 AMS Classification: 11B37

Abstract

In this paper we obtain some identities containing generalized Fibonacciand Lucas numbers. Some of them are new and some are well known.By using some of these identities we give some congruences concerninggeneralized Fibonacci and Lucas numbers such asV 2mn+r ≡ (−(−t)m ) n V r (mod Vm ), U 2mn+r ≡ (− (−t)m ) n U r (mod Vm ), and V 2mn+r ≡ (−t)mn V r (mod Um ), U 2mn+r ≡ (−t)mn U r (mod Um ).

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Cite This Article

Şiar, Z., Keskin, R. (2013). Some New Identities Concerning Generalized Fibonacciand Lucas Numbers. Hacettepe Journal of Mathematics and Statistics, Volume: 42 Issue: 3. https://ajindex.com/articles/1403479

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