USAMO 1973 Problem 2

The sequence $a_{n}$ is defined by $a_{1}=a_{2}=1, a_{n+2}=a_{n+1}+2 a_{n}$. The sequence $b_{n}$ is defined by $b_{1}=1, b_{2}=7$, $b_{n+2}=2 b_{n+1}+3 b_{n}$. Show that the only integer in both sequences is 1 .