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\title{Homework 1: Due Friday January 19th 2018\\
MTH 310 001 W18}
\author{YOUR NAME HERE}
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Solutions must be typed using LaTeX.
Remember to provide justification and write in complete sentences for all responses unless otherwise noted. \\
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\item Sec. 1.1 Problem 2 (a)-(c): Find the quotient $q$ and remainder $r$ when $a$ is divided by $b$, without using technology. Check your answers. (Not need to write complete sentences.)
\begin{center}
\begin{tabular}{lll} (a) $a=-51$; $b=6$ & (b) $a=302$; $b=19$ & (c) $a=2000$; $b=17$\end{tabular}
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\begin{proof}
Type your answer here!
\end{proof}
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\item Sec. 1.1 Problem 5: Let $a$ be any integer and let $b$ and $c$ be positive integers. Suppose that when $a$ is divided by $b$, the quotient is $q$ and the remainder is $r$, so that
\[ a=bq+r \text{ and } 0\le r