even_and_odd_quiz.tex

\yourname

\activitytitle{Quiz on even and odd}{15 points}

\noindent Work hard to write really nice proofs.

\blist{3.5in}
\item Show that the product of two odd numbers is odd.

\item Show that for all integers $n$, the quantity $n^2 + 10n + 21$ is either odd or is a multiple of 4.

\item The numbers $0, 1, 4, 9, 16, 25, \ldots$ are called perfect squares.  The differences between consecutive perfect squares are $1, 3, 5, 7, 9, \ldots$.
Show that the difference between consecutive perfect squares is always an odd number.


\elist
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