HW5 Problem Set 
3mar16


\begin{document}
\maketitle

For your convenience, here is transcript of the problems for this homework.

\begin{itemize}
\item[6.8] Use Euclid's Algorithm to find the GCD and check by the PFT.
\item[6.8a] $gcd(126,224)$
\item[6.8b] $gcd(221,299)$
\item[6.9] Find all solutions for these Diophantine equations.
\item[6.9a] $17x+13y=220$
\item[6.9b] $21x+15y=93$
\item[6.9c] $60x+42y=104$
\item[6.9d] $588x+231y=63$
\item[6.17] Prove that $gcd(a+b,a-b)=gcd(2a,a-b)=gcd(a+b, 2b)$
\item[6.18] Suppose $gcd(a,b)=1$. Does this determine $gcd(a^2,b^2)$? $gcd(a,2b)$?.
\item[6.28] Suppose that $gcd(a,b)=1 \wedge a|n \wedge b|n \Rightarrow ab|n$. (If you don't use
the PFT for this, then you are not following directions.
\item[Extra Credit] Why is the first hypothesis necessary?
\end{itemize}

\end{document}