On repdigits as product of consecutive Fibonacci numbers
Diego Marques, Alain Togbé · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 2012
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).