Let (F$_{n}$)$_{n\geq0}$ be the Fibonacci sequence. In 2000, F.
Luca proved that F10 = 55 is the largest repdigit (i.e. a number with
only one distinct digit in its decimal expansion) in the Fibonacci
sequence. In this note, we show that if Fn · · · F$_{n+(k-1)}$ is
a repdigit, with at least two digits, then (k, n) = (1, 10).
