Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers
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...
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Sakarya University
2023-10-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/2894199 |
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| author | Fatih Erduvan Merve Güney Duman |
| author_facet | Fatih Erduvan Merve Güney Duman |
| author_sort | Fatih Erduvan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ee47595a7b154109a2daed2ed395e2be |
| institution | OA Journals |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Sakarya University |
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| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-ee47595a7b154109a2daed2ed395e2be2025-08-20T01:57:40ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-10-012751122112710.16984/saufenbilder.123557128Mulatu Numbers Which Are Concatenation of Two Fibonacci NumbersFatih Erduvanhttps://orcid.org/0000-0001-7254-2296Merve Güney Duman0https://orcid.org/0000-0002-6340-4817SAKARYA UNIVERSITY OF APPLIED SCIENCES, FACULTY OF TECHNOLOGYLet (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.https://dergipark.org.tr/tr/download/article-file/2894199mulatu and fibonacci numberslinear forms in logarithmsexponential diophantine equationslinear forms in logarithmsmulatu and fibonacci numbersreduction methodexponantial diophantine equations |
| spellingShingle | Fatih Erduvan Merve Güney Duman Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi mulatu and fibonacci numbers linear forms in logarithms exponential diophantine equations linear forms in logarithms mulatu and fibonacci numbers reduction method exponantial diophantine equations |
| title | Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers |
| title_full | Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers |
| title_fullStr | Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers |
| title_full_unstemmed | Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers |
| title_short | Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers |
| title_sort | mulatu numbers which are concatenation of two fibonacci numbers |
| topic | mulatu and fibonacci numbers linear forms in logarithms exponential diophantine equations linear forms in logarithms mulatu and fibonacci numbers reduction method exponantial diophantine equations |
| url | https://dergipark.org.tr/tr/download/article-file/2894199 |
| work_keys_str_mv | AT fatiherduvan mulatunumberswhichareconcatenationoftwofibonaccinumbers AT merveguneyduman mulatunumberswhichareconcatenationoftwofibonaccinumbers |