Nurettin Irmak and Alain Togbé
Notes on Number Theory and Discrete Mathematics, ISSN 13105132
Volume 24, 2018, Number 3, Pages 42—49
DOI: 10.7546/nntdm.2018.24.3.95102
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Authors and affiliations
Nurettin Irmak
Mathematics Department, Art and Science Faculty
Nigde Ömer Halisdemir University, Nigde, Turkey
Alain Togbé
Department of Mathematics, Purdue University Northwest
1401 S. U. S. 421., Westville, IN 46391, United States
Abstract
Let (𝐿^{𝑛})^{𝑛≥0} be the Lucas sequence. D. Marques and A. Togbé [7] showed that if 𝐹_{𝑛}…𝐹_{𝑛+𝑘−1} is a repdigit with at least two digits, then (𝑘, 𝑛) = (1, 10), where (𝐹_{𝑛})_{≥0} is the Fibonacci sequence. In this paper, we solve the equation 𝐿_{𝑛}…𝐿_{𝑛+𝑘−1} = 𝑎 (︂10^{𝑚} − 1) / 9, where 1 ≤ 𝑎 ≤ 9, 𝑛, 𝑘 ≥ 2 and 𝑚 are positive integers.
Keywords
 Lucas numbers
 Repdigits
2010 Mathematics Subject Classification
 11A63
 11B39
 11B50
References
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Cite this paper
Irmak, N., & Togbé, A. (2018). On repdigits as product of consecutive Lucas numbers, Notes on Number Theory and Discrete Mathematics, 24(3), 95102, doi: 10.7546/nntdm.2018.24.3.95102.