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Found problems: 1

2024 AMC 10, 24
Tags: modular , number theory
Let \[P(m)=\frac{m}{2} + \frac{m^2}{4}+ \frac{m^4}{8} + \frac{m^8}{8}.\] How many of the values of $P(2022)$, $P(2023)$, $P(2024)$, and $P(2025)$ are integers? $ \textbf{(A) }0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4 \qquad $