Advanced Studies: Euro-Tbilisi Mathematical Journal

Products of three Fibonacci numbers that are repdigits

M. Alan, K. Simsek Alan

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 F_nF_mF_l = a ( 10^d-1 / 9 ), 1≤l≤m≤n and 1≤a≤9.


Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16(4) (2023), pp. 57-66