Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915483236696064 |
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| author | Ddamulira, Mahadi |
| author_facet | Ddamulira, Mahadi |
| contents | The Tribonacci-Lucas sequence $\{S_n\}_{n\ge 0}$ is defined by the linear recurrence relation $S_{n+3} = S_{n+2} + S_{n+1} + S_n$, for $ n\ge 0 $, with the initial conditions $S_0 =S_2= 3$ and $S_1 = 1$. A palindromic number is a number that remains the same when its digits are reversed. This paper uses Baker's theory for nozero lower bounds for linear forms in logarithms of algebraic numbers, and reduction methods involving the theory of continued fraction to determine all Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits Ddamulira, Mahadi Number Theory 11B39, 11D61, 11J86 The Tribonacci-Lucas sequence $\{S_n\}_{n\ge 0}$ is defined by the linear recurrence relation $S_{n+3} = S_{n+2} + S_{n+1} + S_n$, for $ n\ge 0 $, with the initial conditions $S_0 =S_2= 3$ and $S_1 = 1$. A palindromic number is a number that remains the same when its digits are reversed. This paper uses Baker's theory for nozero lower bounds for linear forms in logarithms of algebraic numbers, and reduction methods involving the theory of continued fraction to determine all Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits. |
| title | Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits |
| topic | Number Theory 11B39, 11D61, 11J86 |
| url | https://arxiv.org/abs/2509.05984 |