AT-OEMO-FED1 2008 Problem 3

Let $p > 1$ be a natural number. Consider the set $F_p$ of all non-constant sequences of non-negative integers that satisfy the recursive relation $a_{n+1} = (p+1)a_n - pa_{n-1}$ for all $n > 0$ . Show that there exists a sequence ( $a_n$ ) in $F_p$ with the property that for every other sequence ( $b_n$ ) in $F_p$ , the inequality $a_n \le b_n$ holds for all $n$ .