Products of three Fibonacci numbers that are repdigits

Abstract

Let (F-n)(n >= 0) be a Fibonacci sequence. A non-negative integer whose digits are all equal is called a repdigit and any non-zero repdigit is of the form a (10(d) -1/9) where 1 <= a <= 9 and 1 <= d. In this paper, we search all repdigits that can be written as products of three Fibonacci numbers. As a mathematical expression, we find all non-negative integer solutions (n, m, l, a, d) of the Diophantine equation FnFmFl = a (10(d) -1/9) , 1 <= l <= m <= n and 1 <= a <= 9..