Rational root theorem

Suppose $𝑓 (𝑥) = \sum 𝑛 𝑖 = 0 𝑎 𝑖 𝑥 𝑖 \in ℤ [𝑥]$ has a rational root $𝑝 / 𝑞$ with $g c d {𝑝, 𝑞} = 1$ . Then $𝑝 ∣ 𝑎 0$ and $𝑞 ∣ 𝑎 𝑛$ . alg This is a special case of Gauß’s lemma.