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\noindent{\Large{\textsc{Intro to Abstract Mathematics\hfill Assignment 8.2  \\ Spring 2020 \hfill Due April 1}}}

\large

\vspace{1cm}



\begin{exercise}
Use B\'ezout's Lemma to prove Euclid's Lemma:  for all $a, b, c \in \N$, if $a|bc$ and $\gcd(a,b) = 1$, then $a|c$.  [{\em Suggestion:}  Write $1 = xa + yb$, then multiply through by $c$.]
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\begin{exercise}
For each pair $\{a, b \}$, compute $\gcd(a,b)$ and find $x, y \in \Z$ so that $\gcd(a,b) = xa + yb$.

\begin{center}
\begin{tabular}{rlcrlcrl}
\bf a. & $\{ 36, 210 \}$ & \hspace{2cm} & \bf b. & $\{ 105, 165 \}$ & \hspace{2cm} & \bf c. & $\{55, 89 \}$
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\end{exercise}

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