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

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.