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\centerline{\bf THEORY OF NUMBERS, Math 115 A}
\centerline{\bf Homework 4 Due Wednesday October 23}
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\begin{enumerate}

\item Using the Fermat factorization method, factor each of the
following positive integers: 73, 8051, 46009, 3200399.

\item Factoring $kn$ by the Fermat factorization method, where
$k$ is a small positive integer, is sometimes easier than factoring
$n$ by this method. Show it is easier to factor $3(901)$ than to
factor $901$.

\item A student returning from Europe changes his French and Swiss
francs into US. money. If he receives 17.06, and received 19 cents
for each French and 59 cents for each Swiss franc, how much of each
type of currency did he exchange?

\item Find all integer solutions of the linear diophantine equations

a) $2x_1+5x_2+4x_3+3x_4=5$

b) $15x_1+6x_2+10x_3+21x_4+35x_5=1$

\item The post office of Davis is left with stamps of only two
values. They discover that there are only 33 postage amounts that 
cannot be made up using these stamps, including 46 cents. What
are the values of the remaining stamps?

\item Write a MAPLE program that finds the solution of a linear
diophantine equation in two variables. Include a print out of
the program and verify it is correct in a couple of instances.

\end{enumerate}

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