1990 AHSME Problems/Problem 30

Let $R_n=\frac{1}{2}(a^n+b^n)$ for each non-negative integer $n$ where $a=3+2\sqrt{2}$ and $b=3-2\sqrt{2}$ . The value of $R_{12345}$ is an integer. What is its units digit? These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.