Fibonacci numbers which are concatenation of three Fibonacci or Lucas numbers

In this note, we show that there is no Fibonacci number that can be expressed as a concatenation of three Fibonacci or Lucas numbers under a certain constraint. That is, we solve to the Diophantine equations Fn = 10d+lFm1 + 10lFm2 + Fm3 and Fn = 10d+lLm1 + 10lLm2 + Lm3 in non-negative integers (n, m1, m2, m3) with m2 ≤ m1, where d and l represent the number of digits of the (Fm2 , Lm2) and (Fm3, Lm3), respectively. Moreover, we give these equations as a problem to the researchers without the constraint m2 ≤ m1.