English

Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits

Number Theory 2025-09-09 v1

Abstract

The Tribonacci-Lucas sequence {Sn}n0\{S_n\}_{n\ge 0} is defined by the linear recurrence relation Sn+3=Sn+2+Sn+1+SnS_{n+3} = S_{n+2} + S_{n+1} + S_n, for n0 n\ge 0 , with the initial conditions S0=S2=3S_0 =S_2= 3 and S1=1S_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.

Keywords

Cite

@article{arxiv.2509.05984,
  title  = {Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits},
  author = {Mahadi Ddamulira},
  journal= {arXiv preprint arXiv:2509.05984},
  year   = {2025}
}

Comments

12 pages