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{{\Large\bf MODERN ALGEBRA I}\\
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{\Large\bf HOMEWORK ASSIGNMENT II}\\
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{\bf (Turn in underlined problems.)}}
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{\bf 
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\underline{\large\bf CHAPTER}\makebox[2in]{}\=\underline{\large\bf PROBLEMS}\\

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\noindent
1 \> \underline{1.31}, \underline{1.32},
\underline{1.35}
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\underline{\large\bf ADDITIONAL PROBLEMS}
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{\bf 

\underline{1.} Explain how the Euclidean algorithm can be
used to find integers $x, y$ and $z$ such that $12x+15y+20z=1$.

\medskip

\underline{2.} Consider the following two (different) definitions.
\begin{quote}
{\rm A number $p$ is {\bf prime} if whenever $p\mid ab$,
then $p\mid a$ or $p\mid b$.}
\end{quote}
\begin{quote}
{\rm A number $q$ is {\bf irreducible} if whenever $q=ab$,
then $a=\pm 1$ or $b=\pm 1$.}
\end{quote}
Show that an integer is prime if and only if it is irreducible.


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