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Problem 57 (Eisenstein's Criterion)
Let $f(x)=a_nx^n + \cdots +a_1x +a_0$. Prove that if there is a prime $p$ such that $p$ divides every coefficient but $a_n$ and $p^2$ does not divide $a_0$, then $f(x)$ is irreducible over $\mathbb{Q}$.
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