Relationships Among Repdigit Sets Derived From Fibonacci And Lucas Products In Bases 2 To 10

2026/07/21 by Harunori Nakayama
Physics and Astronomy · Computer Science · Mathematics · #Advanced Mathematical Theories and Applications #Graph Labeling and Dimension Problems #Graph theory and applications

paper · doi:10.1080/00150517.2026.2638777

Abstract

This paper determines all repdigits in bases 2 to 10 expressible as the product of a Fibonacci number and a Lucas number. To prove our results, we use Baker’s theory, a generalized Baker–Davenport reduction, and an exhaustive search. We also investigate the set-theoretic relationships among these repdigits and those previously obtained from products of two Fibonacci numbers and of two Lucas numbers. In particular, we identify a repdigit set 20,32,35,88,91 that occurs only as products of a Fibonacci number and a Lucas number.

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