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AIME 2017 II #8 — Exponential Polynomial mod Integer

2525MasterAlgebraNumber TheoryCounting Principles

AIME II · 2017 · Problem 8

Find the number of positive integers $n$ less than $2017$ such that $$1+n+\frac{n^2}{2!}+\frac{n^3}{3!}+\frac{n^4}{4!}+\frac{n^5}{5!}+\frac{n^6}{6!}$$ is an integer. [[2017 AIME II Problems/Problem 8 | Solution]]
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