Question 24
Let
$$
\begin{aligned} P(m) &= \frac{m}{2} + \frac{m^2}{4} \\ &\quad {}+ \frac{m^4}{8} + \frac{m^8}{8}. \end{aligned}
$$
How many of the values of $P(2022),$ $P(2023),$ $P(2024),$ and $P(2025)$ are integers?
$$
\begin{aligned} P(m) &= \frac{m}{2} + \frac{m^2}{4} \\ &\quad {}+ \frac{m^4}{8} + \frac{m^8}{8}. \end{aligned}
$$
How many of the values of $P(2022),$ $P(2023),$ $P(2024),$ and $P(2025)$ are integers?