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Dergiler / Sakarya University Journal of Science / 2026 / Volume: 27 Issue: 5

Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers

Fatih Erduvan0000-0001-7254-2296
Merve Güney Duman(SAKARYA UNIVERSITY OF APPLIED SCIENCES, FACULTY OF TECHNOLOGY)0000-0002-6340-4817
Sayfa
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Yayın Tarihi
2023-10-18
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Here the main tools are linear forms in logarithms and Baker Davenport basis reduction method.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2.
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Temel Bulgular & Veri:In this paper, we showed that all Mulatu numbers, that are concatenations of two Fibonacci numbers are 11,28.
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Sonuç & Katkı:Here the main tools are linear forms in logarithms and Baker Davenport basis reduction method.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Mulatu and Fibonacci numbers · linear forms in logarithms · exponential Diophantine equations

Abstract

Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2. In this paper, we showed that all Mulatu numbers, that are concatenations of two Fibonacci numbers are 11,28. That is, we solved the equation M_k=〖10〗^d F_m+F_n, where d indicates the number of digits of F_n. We found the solutions of this equation as (k,m,n,d)∈{(4,2,2,1),(6,3,6,1)}. Moreover the solutions of this equation displayed as M_4=(F_2 F_2 ) ̅=11 and M_6=(F_3 F_6 ) ̅=28. Here the main tools are linear forms in logarithms and Baker Davenport basis reduction method.

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Bu Makaleye Atıf Yap

Erduvan, F., Duman, M. G. (2023). Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers. Sakarya University Journal of Science, Volume: 27 Issue: 5. https://doi.org/10.16984/saufenbilder.1235571

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Kaynakça (10)

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