## A Rational Root of a Monic Polynomial with Integer Coefficients is an Integer

## Problem 489

Suppose that $\alpha$ is a rational root of a monic polynomial $f(x)$ in $\Z[x]$.

Prove that $\alpha$ is an integer.

Suppose that $\alpha$ is a rational root of a monic polynomial $f(x)$ in $\Z[x]$.

Prove that $\alpha$ is an integer.