80 lines
2.2 KiB
TeX
80 lines
2.2 KiB
TeX
\documentclass[12pt,a4paper,german]{article}
|
|
\usepackage{url}
|
|
%\usepackage{graphics}
|
|
\usepackage{times}
|
|
\usepackage[T1]{fontenc}
|
|
\usepackage{ngerman}
|
|
\usepackage{float}
|
|
\usepackage{diagbox}
|
|
\usepackage[utf8]{inputenc}
|
|
\usepackage{geometry}
|
|
\usepackage{amsfonts}
|
|
\usepackage{amsmath}
|
|
\usepackage{cancel}
|
|
\usepackage{wasysym}
|
|
\usepackage{csquotes}
|
|
\usepackage{graphicx}
|
|
\usepackage{epsfig}
|
|
\usepackage{paralist}
|
|
\usepackage{tikz}
|
|
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
|
|
|
|
%%%%%%%%%% Fill out the the definitions %%%%%%%%%
|
|
\def \name {Valentin Brandl} %
|
|
\def \matrikel {108018274494} %
|
|
\def \pname {Marvin Herrmann} %
|
|
\def \pmatrikel {108018265436} %
|
|
\def \gruppe {2 (Mi 10-12 Andre)}
|
|
\def \qname {Pascal Brackmann}
|
|
\def \qmatrikel {108017113834} %
|
|
\def \uebung {9} %
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
% DO NOT MODIFY THIS HEADER
|
|
\newcommand{\hwsol}{
|
|
\vspace*{-2cm}
|
|
\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
|
|
\noindent \pmatrikel \quad \pname \\
|
|
\noindent \qmatrikel \quad \qname \\
|
|
\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
|
|
}
|
|
|
|
\begin{document}
|
|
%Import header
|
|
\hwsol
|
|
|
|
\section*{Aufgabe 9.3}
|
|
|
|
\begin{enumerate}[1.]
|
|
|
|
\item
|
|
\begin{tabular}{|c|c|c|}
|
|
\hline
|
|
$eea(a,b)$ & $(d',x',y')$ & $(d,x,y)$ \\\hline\hline
|
|
$eea(84,15)$ & $(3,-1,2)$ & $(3,2,-11)$ \\\hline
|
|
$eea(15,9)$ & $(3,1,-1)$ & $(3,-1,2)$ \\\hline
|
|
$eea(9,6)$ & $(3,0,1)$ & $(3,1,-1)$ \\\hline
|
|
$eea(6,3)$ & $(3,1,0)$ & $(3,0,1)$ \\\hline
|
|
$eea(3,0)$ & & $(3,1,0)$ \\\hline
|
|
\end{tabular}
|
|
|
|
$ggt(84,15) = 84 * 2 + 15 * (-11) = 3$
|
|
|
|
\item
|
|
\begin{tabular}{|c|c|c|}
|
|
\hline
|
|
$eea(a,b)$ & $(d',x',y')$ & $(d,x,y)$ \\\hline\hline
|
|
$eea(93,32)$ & $(1,10,-11)$ & $(1,-11,32)$ \\\hline
|
|
$eea(32,29)$ & $(1,-1,10)$ & $(1,10,-11)$ \\\hline
|
|
$eea(29,3)$ & $(1,1,-1)$ & $(1,-1,10)$ \\\hline
|
|
$eea(3,2)$ & $(1,0,1)$ & $(1,1,-1)$ \\\hline
|
|
$eea(2,1)$ & $(1,1,0)$ & $(1,0,1)$ \\\hline
|
|
$eea(1,0)$ & & $(1,1,0)$ \\\hline
|
|
\end{tabular}
|
|
|
|
$ggt(93,32) = 93 * (-11) + 32 * 32 = 1$
|
|
|
|
\end{enumerate}
|
|
|
|
\end{document}
|