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\title{Math 480 (Spring 2007): Homework 5}
\author{\bf Due: Monday, April 30}
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\noindent{\bf There are 3 problems.} Each problem is worth 6 points
and parts of multipart problems are worth equal amounts.  You may work
with other people and use a computer, unless otherwise stated.  Acknowledge
those who help you.\\

\begin{enumerate}

\item Encode the message {\tt NUMBER THEORY} as a single number in base 27,
where 0 corresponds to a space, A to 1, B to 2 and so on.

\item How many solutions does the following system of congruences have?
\begin{eqnarray*}
 x&\equiv& 3 \pmod{18}\\
 x&\equiv& 2 \pmod{3}\\
 x&\equiv& 1 \pmod{6}
\end{eqnarray*}

\item In class I mentioned the famous open problem
that there are infinitely many primes $p$ such that $(p-1)/2$
is also prime.   Is it reasonable to conjecture that there are 
infinitely many primes $p$ such that $p\con 1\pmod{3}$ and
$(p-1)/3$ is prime?
\end{enumerate}

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