[[Algebraic number theory MOC]]
# Rational root theorem

Suppose $f(x) = \sum_{i=0}^n a_{i}x^i \in \mathbb{Z}[x]$
has a rational root $p / q$ with $\gcd \{ p,q \} = 1$.
Then $p \mid a_{0}$ and $q \mid a_{n}$. #m/thm/num/alg 
This is a special case of [[Gauß's lemma]].

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