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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

On square Tribonacci Lucas numbers

Nurettin Irmak
Pages
1652–1657
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3.
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Key Findings & Data:The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3.
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Conclusion & Impact:In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tribonacci sequence · Tribonacci Lucas sequence · squares

Abstract

The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).

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Cite This Article

Irmak, N. (2022). On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1652–1657. https://ajindex.com/articles/529528

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References (6)

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