MathNet 2025 — Part 01 (100 complete bilingual questions) Question 8

Let $k \gt 2$ be a given positive integer. Find all positive integers $d$, for which there exists a polynomial $P(x)$ with integer coefficients such that $\deg P(x) = d$ and $11^k \mid 2025^n + P(n)$ for all positive integers $n \gt k$.