%p10.tex: 
%begin macros
\baselineskip=14pt
\parskip=10pt
\magnification=\magstephalf
\parindent=0pt
\overfullrule=0in
\def\frac#1#2{{#1 \over #2}}
\def\g{\bigtriangledown}
\def\S{\cal S}
\nopagenumbers
%end macros
 

\centerline
{
\bf Attendance Quiz \# 10 for Dr. Z.'s Number Theory
}
\bigskip
{\bf NAME:} (print!) $\underline
{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\bigskip
{\bf E-MAIL ADDRESS:} (print!) 
$\underline
{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\bigskip

{\bf 1.} Without actually solving, 
find out how many solutions there are in $\{0,1, \dots n-1\}$ where $n$ is the modulo.

{\bf i.} $21x \equiv 12 \pmod{33}$

{\bf ii.} $5^{10}x \equiv 2^{10} \pmod{13^{30}}$


\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip
\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip
\bigskip\bigskip\bigskip\bigskip\bigskip\bigskip


{\bf 2.}: Find, or explain why it does not exist $4^{-1} \pmod {21}$.


\end






