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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 21 Sayı: 2

Tribonacci numbers as sum or difference of powers of 2

Fatih Erduvan(İZMİT NAMIK KEMAL ANADOLU LİSESİ)0000-0001-7254-2296
Pages
147–151
Publication Date
2025-06-27
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AI Summary & Key Takeaways

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

Our findings reveal specific instances where such representations are possible, including examples like the seventh Tribonacci number expressed both as the sum and the difference of powers of 2.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper investigates Tribonacci numbers can be expressed as either the sum or difference of two distinct powers of 2.
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Key Findings & Data:Namely, we address the problem of expressing Tribonacci numbers in the form T_n=2^x±2^y in positive integers with 1≤y≤x.
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Conclusion & Impact:Our findings reveal specific instances where such representations are possible, including examples like the seventh Tribonacci number expressed both as the sum and the difference of powers of 2.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Diophantine equations · Tribonacci numbers · Baker’s Theory

Abstract

This paper investigates Tribonacci numbers can be expressed as either the sum or difference of two distinct powers of 2. Namely, we address the problem of expressing Tribonacci numbers in the form T_n=2^x±2^y in positive integers with 1≤y≤x. Our findings reveal specific instances where such representations are possible, including examples like the seventh Tribonacci number expressed both as the sum and the difference of powers of 2. Additionally, we identify Tribonacci numbers that can be represented as the differences of Mersenne numbers, specifically, the numbers 2, 4, 24, and 504. These results enhance the understanding of the structural properties of Tribonacci sequences and their relationships with exponential and Mersenne-based number systems.

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Cite This Article

Erduvan, F. (2025). Tribonacci numbers as sum or difference of powers of 2. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 21 Sayı: 2, 147–151. https://doi.org/10.18466/cbayarfbe.1528991

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