Question 183
The sequence $a_1, a_2, \dots$ is defined by the equalities $a_1 = 2$, $a_2 = 12$ and $a_{n+1} = 6a_n - a_{n-1}$ for every positive integer $n \ge 2$. Prove that no member of this sequence is equal to a perfect power (greater than one) of a positive integer.