INMO 1996 Problem 5

Define a sequence $(a_n)_{n \geq 1}$ by $a_1 =1$ and $a_2 =2$ and $a_{n+2} = 2 a_{n+1} - a_n + 2$ for $n \geq 1$ . prove that for any $m$ , $a_m a_{m+1}$ is also a term in this sequence.