division_elimination_quiz.tex

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\activitytitle{Quiz on Division Algorithm, Contrapositive, Elimination, and Contradiction}{}

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\item 
The goal is to show that if an integer $n$ is a multiple of 3 and also a multiple of 5, then it is a multiple of 15.

We can write $n=3i=5j$ for integers $i$ and $j$.

Use three cases and eliminate two of them to show that $j$ is a multiple of 3.
Be very clear about where the three cases come from and about your logic.

\item
Suppose that $n$ is an integer and that $n^2$ is a multiple of 15.
Use results we showed in class and the result above to show that $n$ is a multiple of 15.
Explain clearly.



\item Use a proof by contradiction to show that $\sqrt{15}$ is irrational.


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