Nurettin Irmak and Alain Togbé
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 24, 2018, Number 3, Pages 42—49
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Let (𝐿𝑛)𝑛≥0 be the Lucas sequence. D. Marques and A. Togbé  showed that if 𝐹𝑛…𝐹𝑛+𝑘−1 is a repdigit with at least two digits, then (𝑘, 𝑛) = (1, 10), where (𝐹𝑛)≥0 is the Fibonacci sequence. In this paper, we solve the equation 𝐿𝑛…𝐿𝑛+𝑘−1 = 𝑎 (︂10𝑚 − 1) / 9, where 1 ≤ 𝑎 ≤ 9, 𝑛, 𝑘 ≥ 2 and 𝑚 are positive integers.
- Lucas numbers
2010 Mathematics Subject Classification
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Cite this paperAPA
Irmak, N., & Togbé, A. (2018). On repdigits as product of consecutive Lucas numbers, Notes on Number Theory and Discrete Mathematics, 24(3), 95-102, doi: 10.7546/nntdm.2018.24.3.95-102.Chicago
Irmak, Nurettin, and Alain Togbé. “On Repdigits as Product of Consecutive Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 24, no. 3 (2018): 95-102, doi: 10.7546/nntdm.2018.24.3.95-102.MLA
Irmak, Nurettin, and Alain Togbé. “On Repdigits as Product of Consecutive Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 24.3 (2018): 95-102. Print, doi: 10.7546/nntdm.2018.24.3.95-102.