Fibonacci or Lucas Numbers Which are Products of Two Repdigits in Base b

Abstract

In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base b. It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are F12= 144 and L15= 1364 , respectively. Also, we have the presentation F12=144=6×(3+3·7)=(6)7×(33)7=4×(4+4·8)=(4)8×(44)8and L15=1364×(22222)4=2×(2+2·4+2·42+2·43+2·44). © 2021, Sociedade Brasileira de Matemática.