Question 21
There is a unique ordered triple $(a, k, m)$ of nonnegative integers such that
$$
\begin{aligned} &\small \frac{4^a + 4^{a+k} + 4^{a+2k} + \cdots + 4^{a+mk}}{2^a + 2^{a+k} + 2^{a+2k} + \cdots + 2^{a+mk}} \\ &= 964. \end{aligned}
$$
What is $a + k + m?$
$$
\begin{aligned} &\small \frac{4^a + 4^{a+k} + 4^{a+2k} + \cdots + 4^{a+mk}}{2^a + 2^{a+k} + 2^{a+2k} + \cdots + 2^{a+mk}} \\ &= 964. \end{aligned}
$$
What is $a + k + m?$