Crypto edits
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@ -21,15 +21,6 @@ In other words, we can divide $a$ by $b$ to get $q$ remainder $r$.
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For any integers $a, b, c$, \par
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$\gcd(ac + b, a) = \gcd(a, b)$
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\problem{}
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Compute the gcd of 12 and 976.
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\begin{solution}
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$976 = 3 \times 324 + 4 = 3 \times 4 \times 81 + 4$
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So, $\gcd(a, b) = 4$
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\end{solution}
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\vfill
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\problem{The Euclidean Algorithm}<euclid>
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Using the two theorems above, detail an algorithm for finding $\gcd(a, b)$. \par
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Then, compute $\gcd(1610, 207)$ by hand. \par
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@ -109,7 +100,6 @@ We now want to write the 2 in the last equation in terms of 20 and 14.
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\begin{solution}
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Using the output of the Euclidean Algorithm, we can use substitution and a bit of algebra to solve such problems. Consider the following example:
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\begin{multicols}{2}
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@ -139,6 +129,10 @@ We now want to write the 2 in the last equation in terms of 20 and 14.
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$\gcd(541, 34) = 541(11) + 34(-175)$
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\end{solution}
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\begin{solution}
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\huge
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This problem is too hard. Break it into many.
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\end{solution}
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\vfill
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\pagebreak
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