@Article{JMS-55-1,
author = {Şiar, Zafer and Fatih, Erduvan and Refik, Keskin},
title = {Repdigits Base $b$ as Difference of Two Fibonacci Numbers},
journal = {Journal of Mathematical Study},
year = {2022},
volume = {55},
number = {1},
pages = {84--94},
abstract = {<p style="text-align: justify;">In this paper, we find all repdigits expressible as difference of two Fibonacci numbers in base $b$ for $2\leq b\leq10.$ The largest repdigits in base $b$, which can be written as difference of two Fibonacci numbers are \begin{align*}&amp;F_{9}-F_{4}=34-3=31=(11111)_{2},~~~~~~\text{ }F_{14}-F_{7}=377-13=364=(111111)_{3},\\&amp;F_{14}-F_{7}=377-13=364=(222)_{4},~~ \text{ }F_{9}-F_{4}=34-3=31=(111)_{5},\\&amp;F_{11}-F_{4}=89-3=86=(222)_{6},~~~~~~~~\text{ }F_{13}-F_{5}=233-5=228=(444)_{7},\\&amp;F_{10}-F_{2}=55-1=54=(66)_{8},~~~~~~~~~~\text{ }F_{14}-F_{7}=377-13=364=(444)_{9},\end{align*} and $$F_{15}-F_{10}=610-55=555=(555)_{10}.$$</p><p style="text-align: justify;">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 $F_{15}=610=555+55=555+F_{10}.$<br/></p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v55n1.22.07},
url = {https://global-sci.com/article/87642/repdigits-base-b-as-difference-of-two-fibonacci-numbers}
}