Repdigits Base b as Difference of Two Fibonacci Numbers
Year: 2022
Author: Zafer Şiar, Fatih Erduvan, Refik Keskin
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 84–94
Abstract
In this paper, we find all repdigits expressible as difference of two Fibonacci numbers in base b for 2≤b≤10. The largest repdigits in base b, which can be written as difference of two Fibonacci numbers are F9−F4=34−3=31=(11111)2, F14−F7=377−13=364=(111111)3,F14−F7=377−13=364=(222)4, F9−F4=34−3=31=(111)5,F11−F4=89−3=86=(222)6, F13−F5=233−5=228=(444)7,F10−F2=55−1=54=(66)8, F14−F7=377−13=364=(444)9, and F15−F10=610−55=555=(555)10.
As a result, it is shown that the largest Fibonacci number which can be written as a sum of a repdigit and a Fibonacci number is F15=610=555+55=555+F10.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n1.22.07
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 84–94
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Fibonacci numbers repdigit Diophantine equations linear forms in logarithms.
Author Details
Zafer Şiar Email
Fatih Erduvan Email
Refik Keskin Email
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AIMS Mathematics, Vol. 9 (2024), Iss. 8 P.20173
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