Crypto edits

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2024-10-24 09:33:50 -07:00
parent 8b10780fbe
commit 1609ec919a
3 changed files with 11 additions and 18 deletions

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@ -21,15 +21,6 @@ In other words, we can divide $a$ by $b$ to get $q$ remainder $r$.
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
@ -109,7 +100,6 @@ We now want to write the 2 in the last equation in terms of 20 and 14.
\begin{solution}
Using the output of the Euclidean Algorithm, we can use substitution and a bit of algebra to solve such problems. Consider the following example:
\begin{multicols}{2}
@ -139,6 +129,10 @@ We now want to write the 2 in the last equation in terms of 20 and 14.
$\gcd(541, 34) = 541(11) + 34(-175)$
\end{solution}
\begin{solution}
\huge
This problem is too hard. Break it into many.
\end{solution}
\vfill
\pagebreak