Exercise 12, § 1

For each pair of real numbers $(\theta, \beta)$ there exists an infinite number of triples $(p, q, r)$ of integers such that $r > 0, |q| \leq \frac{1}{2}r$ and

[If $m, n$ are two integers such that $|n\theta - m| < 1/n$ (Exercise 10), take $r = n$ and choose $p, q$ so that $pn + qm$ differs from $n\beta$ by less than $1/2$].