Nurettin Irmak and Alain Togbé
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 21—25
Download PDF (178 Kb)
Authors and affiliations
Let In this paper, we show that the solutions of the equation are , where has at least two digits.
- Diophantine equation
2020 Mathematics Subject Classification
- Adegbindin, C., Luca, F., & Togbé, A. (2019). Lucas numbers as sums of two repdigits. Lithuanian Mathematical Journal, 59, 295–304.
- Adegbindin, C., Luca, F., & Togbé, A. (2020). Pell and Pell–Lucas numbers as sums of two repdigits. Bulletin of the Malaysian Mathematical Sciences Society, Series 2, 43(2), 1253–1271.
- Irmak, N. (2019). On factorials in Perrin and Padovan sequences. Turkish Journal of Mathematics, 43, 2602–2609.
- Irmak, N., & Togbé, A. (2018). On repdigits as product of consecutive Lucas Numbers. Notes on Number Theory and Discrete Mathematics, 24(3), 95–102.
- Luca, F. (2000). Fibonacci and Lucas numbers with only one distinct digit. Portugaliae Mathematica, 50, 243–254.
- Luca, F., Normenyo, B. V., & Togbé, A. (2019). Repdigits as sums of four Pell numbers. Boletin de la Sociedad Matematica Mexicana, 25(2), 249–266.
- Marques, D. (2012). The order of appearance of product of consecutive Fibonacci numbers. Fibonacci Quarterly, 50, 132–139.
- Marques, D., & Lengyel, T. (2014). The 2-adic Order of the Tribonacci Numbers and the Equation Tn = m!. Journal of Integer Sequences, 17, Article 14.10.1.
- Marques, D., & Togbé, A. (2012). On repdigits as product of consecutive Fibonacci numbers. Rendiconti dell’Istituto di matematica dell’Universit di Trieste, 44, 393–397.
- Normenyo, B. V., Luca, F., & Togbé, A. (2018). Repdigits as Sums of Four Fibonacci or Lucas Numbers. Journal of Integer Sequences, 21, Article 18.7.7.
- Rayaguru, S. G., & Panda, G. K. (2018). Repdigits as products of consecutive balancing or Lucas-balancing numbers. Fibonacci Quarterly, 56(4), 319–324.
- Rayaguru, S. G., & Panda, G. K. (2021). Repdigits as sums of two associated Pell numbers. Applied Mathematics E-notes, 21, 402–409.
- Rayaguru, S. G., & Panda, G. K. (2021). Balancing and Lucas-Balancing numbers
expressible as sum of two repdigits. Integers, 21, A7.
- Siar, Z., & Keskin, R. (2020). Repdigits as sums of two Lucas numbers. Applied Mathematics E-Notes, 20, 33–38.
- Received: 11 January 2021
- Revised: 1 October 2022
- Accepted: 17 January 2022
- Online First: 6 February 2022
Cite this paper
Irmak, N., & Togbé, A. (2022). Factorials as repdigits in base b. Notes on Number Theory and Discrete Mathematics, 28(1), 21-25, DOI: 10.7546/nntdm.2022.28.1.21-25.