Question 158
Let
$$
P(m) = \frac{m}{2} + \frac{m^2}{4} + \frac{m^4}{8} + \frac{m^8}{8}.
$$
How many of the values $P(2022)$, $P(2023)$, $P(2024)$, and $P(2025)$ are integers?
$$
P(m) = \frac{m}{2} + \frac{m^2}{4} + \frac{m^4}{8} + \frac{m^8}{8}.
$$
How many of the values $P(2022)$, $P(2023)$, $P(2024)$, and $P(2025)$ are integers?