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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Volume: 50 Issue: 6

On square Tribonacci Lucas numbers

Nurettin Irmak(NIGDE OMER HALISDEMIR UNIVERSITY)0000-0003-0409-4342
Pages
—
Publication Date
2021-12-14
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In this note, we show that 1 1 is the only perfect square in Tribonacci-Lucas sequence for n ≢ 1 ( mod 32 ) n≢1(mod32) and n ≢ 17 ( mod 96 ) . n≢17(mod96).

📌 3 Key Takeaways

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Objective & Hypothesis:The Tribonacci-Lucas sequence { S n } {Sn} is defined by the recurrence relation S n + 3 = S n + 2 + S n + 1 + S n Sn+3=Sn+2+Sn+1+Sn with S 0 = 3 , S 1 = 1 , S 2 = 3.
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Key Findings & Data:The Tribonacci-Lucas sequence { S n } {Sn} is defined by the recurrence relation S n + 3 = S n + 2 + S n + 1 + S n Sn+3=Sn+2+Sn+1+Sn with S 0 = 3 , S 1 = 1 , S 2 = 3.
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Conclusion & Impact:In this note, we show that 1 1 is the only perfect square in Tribonacci-Lucas sequence for n ≢ 1 ( mod 32 ) n≢1(mod32) and n ≢ 17 ( mod 96 ) . n≢17(mod96).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tribonacci sequence · Tribonacci Lucas sequence · squares

Abstract

The Tribonacci-Lucas sequence { S n } {Sn} is defined by the recurrence relation S n + 3 = S n + 2 + S n + 1 + S n Sn+3=Sn+2+Sn+1+Sn with S 0 = 3 , S 1 = 1 , S 2 = 3. S0=3, S1=1, S2=3. In this note, we show that 1 1 is the only perfect square in Tribonacci-Lucas sequence for n ≢ 1 ( mod 32 ) n≢1(mod32) and n ≢ 17 ( mod 96 ) . n≢17(mod96).

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Cite This Article

Irmak, N. (2021). On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 6. https://doi.org/10.15672/hujms.651786

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References (8)

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