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\title{Math 412  Homework 5}
\date{Due date: Oct 2, 2015}
\author{your name}


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Solve the following problems. Please remember to use complete sentences
and good grammar. 



\begin{enumerate}

\item (4 points) Suppose that $n=917, 4x8, 835$, where $x$ is a missing digit. Find all possible values of $x$ so that $n$ is divisible by $k$, where 
$$ k=9, \  k=11, \  \text{ or } \ k=13$$

\item (4 points) Prove that $\phi(mn)=(m,n)\phi([m,n])$. 

\item (4 points) Find all positive integers $n$ so that $\phi(n)|n$.  

\item (4 points) Use Euler-phi-function to show that there are infinitely many primes. 








\end{enumerate}

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