Crypto edits

Advanced/Cryptography/parts/0 euclidean.tex

@@ -17,20 +17,19 @@ Find $\gcd(20, 14)$ by hand.
 Given two integers $a, b$, we can find two integers $q, r$, where $0 \leq r < b$ and $a = qb + r$. \par
 In other words, we can divide $a$ by $b$ to get $q$ remainder $r$.
 
-\begin{instructornote}
-	\ref{divalgo} looks scary on paper, but it's quite simple. \par
-	Doing a small example on the board (like $14 \div 3$) may be a good idea. \par
-
-	\vspace{2mm}
-
-	For those that are new to modular arithmetic, you may want to explain how remainders,
-	clock-face counting, division algorithm, and modular arithmetic are all the same.
-\end{instructornote}
-
 \theorem{}<gcd_abc>
 For any integers $a, b, c$, \par
 $\gcd(ac + b, a) = \gcd(a, b)$
 
+\problem{}
+Compute the gcd of 12 and 976.
+\begin{solution}
+	$976 = 3 \times 324 + 4 = 3 \times 4 \times 81 + 4$
+	So, $\gcd(a, b) = 4$
+\end{solution}
+
+\vfill
+
 \problem{The Euclidean Algorithm}<euclid>
 Using the two theorems above, detail an algorithm for finding $\gcd(a, b)$. \par
 Then, compute $\gcd(1610, 207)$ by hand. \par