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\noindent\emph{\textbf{Score: \underline{\hspace*{1cm}} out of 10\hfill Name: \underline{\hspace*{4.1cm}}}}
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\bf\emph{MATH 221 \--- Foundations of Mathematics \--- Dr. Russell E. Goodman\\
Fall 2010 \--- Take-Home Quiz \#8}\\
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\noindent\emph{This quiz is worth 10 points. Consider the theorem stated below along with the 12 sentences provided on the second page. Rearrange the sentences so the resulting text forms a logical and well-organized proof of the theorem. Please \textbf{literally} cut out the 12 sentences and tape them to this first page in the order you feel is appropriate and turn in the taped quiz \textbf{by 4pm on December 8}.}
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\noindent\emph{\textbf{You are expected to work alone on this quiz, neither giving nor receiving assistance to/from any classmates, friends or professors. Any violation of this expectation will result in a grade of zero on this quiz for all involved parties.}}
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\noindent\textbf{Theorem:} \emph{Every integer greater than 1 is expressible as a product of primes.}
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\item Hence, we see that $n=\left( (p_{1}\cdot p_{2}\cdots p_{s})\cdot(q_{1}\cdot q_{2}\cdots q_{t})\right)$.
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\item But $a$ and $b$ must then be expressible as products of primes due to the minimality of $n$.
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\item It also must be the case that $1