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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we use Baker’s method to show that 4, 16, 64, 208, 976, and 1936 are all k -Fibonacci numbers of the form (3a ± 1)(3b ± 1), where a and b are nonnegative integers
📌 3 Key Takeaways
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Objective & Hypothesis:For k ≥ 2, consider the k -Fibonacci sequence (F(k) n )n≥2−k having initial conditions 0, . . . , 0, 1 (k terms) and each term afterwards is the sum of the preceding k terms.
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Key Findings & Data:The Fibonacci sequence is a special case of (F(k) n )n≥2−k with k = 2 and Tribonacci sequence is (F(k) n )n≥2−k with k = 3.
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Conclusion & Impact:In this paper, we use Baker’s method to show that 4, 16, 64, 208, 976, and 1936 are all k -Fibonacci numbers of the form (3a ± 1)(3b ± 1), where a and b are nonnegative integers
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
For k ≥ 2, consider the k -Fibonacci sequence (F(k) n )n≥2−k having initial conditions 0, . . . , 0, 1 (k terms) and each term afterwards is the sum of the preceding k terms. Some well-known sequences are special cases of this generalization. The Fibonacci sequence is a special case of (F(k) n )n≥2−k with k = 2 and Tribonacci sequence is (F(k) n )n≥2−k with k = 3. In this paper, we use Baker’s method to show that 4, 16, 64, 208, 976, and 1936 are all k -Fibonacci numbers of the form (3a ± 1)(3b ± 1), where a and b are nonnegative integers
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Cite This Article
TOGBÉ, A., GUEYE, A., RIHANE, S. E. (2022). An exponential equation involving k-Fibonacci numbers. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 6, 2664–2677. https://ajindex.com/articles/607425