Minor errors
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@ -28,7 +28,7 @@ $\gcd(ac + b, a) = \gcd(a, b)$
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\problem{}
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\problem{}
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Compute $\gcd(668, 6)$ \hint{$668 = 111 \times 6 + 2$}
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Compute $\gcd(668, 6)$. \hint{$668 = 111 \times 6 + 2$}
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Then, compute $\gcd(3 \times 668 + 6, 668)$.
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Then, compute $\gcd(3 \times 668 + 6, 668)$.
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\vfill
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\vfill
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@ -237,7 +237,7 @@ $|\alpha - \frac ab| \geq |\alpha - \frac{p_n}{q_n}|$
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\problem{Challenge V}
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\problem{Challenge X}
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Prove the following strengthening of Dirichlet's approximation theorem.
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Prove the following strengthening of Dirichlet's approximation theorem.
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If $\alpha$ is irrational, then there are infinitely many rational numbers
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If $\alpha$ is irrational, then there are infinitely many rational numbers
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$\frac{p}{q}$ satisfying $|\alpha - \frac pq| < \frac{1}{2q^2}$.
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$\frac{p}{q}$ satisfying $|\alpha - \frac pq| < \frac{1}{2q^2}$.
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