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.
Harunori Nakayama (Tue,) studied this question.