Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Lucas numbers that are palindromic concatenations of two distinct repdigits

Herbert Batte

Abstract

Let $ \{L_n\}_{n\geq 0} $ be the sequence of Lucas numbers. In this paper, we determine all Lucas numbers that are palindromic concatenations of two distinct repdigits.

Lucas numbers that are palindromic concatenations of two distinct repdigits

Abstract

Let be the sequence of Lucas numbers. In this paper, we determine all Lucas numbers that are palindromic concatenations of two distinct repdigits.
Paper Structure (11 sections, 7 theorems, 66 equations)

This paper contains 11 sections, 7 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Main Results
  4. Methods
  5. Preliminaries
  6. Linear forms in logarithms
  7. Reduction methods
  8. Proof of Theorem \ref{['thm1.1l']}
  9. The low range $n\le 1000$
  10. The case $n> 1000$
  11. The reduction process

Key Result

Theorem 1.1

There is no Lucas number which is a palindromic concatenation of two distinct repdigits.

Theorems & Definitions (11)

  • Theorem 1.1
  • Definition 2.1
  • Theorem 2.1: Matveev, matl
  • Lemma 2.1: Dujella & Pethö, duj
  • Lemma 2.2: Lemma 7 in guz
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • ...and 1 more