A Diophantine equation in k-Fibonacci numbers and repdigits

2018/01/01 by Jhon J. Bravo, Carlos A. Gómez, Florian Luca · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications

paper · doi:10.4064/cm7149-6-2017

crossref issued 2018/01/01 · crossref published 2018/01/01 · crossref published-online 2018/01/01 · openalex publication_date 2018/01/01 · crossref created 2018/03/12 · crossref deposited 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22 · crossref indexed 2026/07/31

Abstract

The k-generalized Fibonacci sequence \F_n^(k)\_n starts with the k values 0,… ,0,1 and each term afterwards is the sum of the k preceding terms. We study which members of this sequence are sums of two repdigts, extending a result of

Citations

• A generalization of a theorem of Baker and Davenport
• THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2

Cited by

• Repdigits in Narayana's Cows Sequence and their Consequences
• k-Fibonacci numbers that are palindromic concatenations of two distinct Repdigits