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2023-10-26 09:42:02 -07:00
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Advanced/Continued Fractions/parts/02 part B.tex
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@ -237,7 +237,7 @@ $|\alpha - \frac ab| \geq |\alpha - \frac{p_n}{q_n}|$
\problem{Challenge V}
\problem{Challenge X}
Prove the following strengthening of Dirichlet's approximation theorem.
If $\alpha$ is irrational, then there are infinitely many rational numbers
$\frac{p}{q}$ satisfying $|\alpha - \frac pq| < \frac{1}{2q^2}$.