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\noindent{\Large{\textsc{Intro to Abstract Mathematics\hfill Assignment 9.1  \\ Spring 2020 \hfill Due April 8}}}

\large

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\begin{exercise}
Use the division algorithm to (finally!) prove that $n \in \Z$ is odd if and only if $n = 2k+1$ for some $k \in \Z$.  [{\em Suggestion:}  What are the possible remainders after division by 2?]
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\begin{exercise}
Let $a, b \in \N^+$, $d = \gcd(a,b)$, and write $a = dm$ and $b = dn$ for some $m, n \in \N^+$.  Prove that $\gcd(m,n) = 1$.  [{\em Suggestion:}  See exercise 7.2.2.]
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