diff --git a/Advanced/Continued Fractions/parts/00 euclidean.tex b/Advanced/Continued Fractions/parts/00 euclidean.tex index ff7e03b..eacf5e1 100755 --- a/Advanced/Continued Fractions/parts/00 euclidean.tex +++ b/Advanced/Continued Fractions/parts/00 euclidean.tex @@ -28,7 +28,7 @@ $\gcd(ac + b, a) = \gcd(a, b)$ \problem{} -Compute $\gcd(668, 6)$ \hint{$668 = 111 \times 6 + 2$} +Compute $\gcd(668, 6)$. \hint{$668 = 111 \times 6 + 2$} Then, compute $\gcd(3 \times 668 + 6, 668)$. \vfill diff --git a/Advanced/Continued Fractions/parts/02 part B.tex b/Advanced/Continued Fractions/parts/02 part B.tex index ad33cb6..6793528 100644 --- a/Advanced/Continued Fractions/parts/02 part B.tex +++ b/Advanced/Continued Fractions/parts/02 part B.tex @@ -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 $|\alpha - \frac pq| < \frac{1}{2q^2}$.