## Definition ## Rational root theorem: Given a natural number $n$ and a degree $n$ [[polynomial function]] $f:\mathbb{Q} \to \mathbb{Q}$ on the [[rational numbers]] with [[integers]] valued coefficients, the [[fiber]] of $f$ at $0$ is inhabited if and only if there exists integers $m$ and $p$ such that $gcd(\vert m \vert, \vert p \vert) = 1$, $m \vert a_0$ and $p \vert a_n$. ## See also ## * [[polynomial function]] * [[rational numbers]] * [[integers]]