KöMaL 2008 B4068

Let $A$, $B$, $C$, $a$, $b$, $c$ denote positive integers, $a^. b^. c$>1. Prove that there exists a positive integer $n$, such that $A^. a^n$+$B^. b^n$+$C^. c^n$ is a composite number.