MathNet 2025 — Part 02 (100 complete bilingual questions) Question 42

The monic polynomial $P(x)$ is called “nice” if its coefficients are in $\{-1, 0, 1\}$. Given a nice polynomial $P(x)$ of degree $2025$ and it is divisible by $x^7 - 1$, what is the maximum number of non-zero coefficients in $P(x)$?