$f(x)=1+x+\frac{x^2}{2!}+\dots+\frac{x^n}{n!}$.
I know that if n is prime, time $n!$ on both sides, since $n$ is prime, Eisenstein criterion shows $f(x)$ is irreducible. Is it also true for arbitrary finite positive integer $n$?
2026-03-30 15:18:04.1774883884
Is this polynomial irreducible over rationals?
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Yes...but I have not seen a short proof.
here is a (not short) proof.