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\title{Math 412  Homework 11}
\date{Due date: Nov 20, 2015}
\author{your name}


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\maketitle

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



\begin{enumerate}


\item Find the simple fraction expression for $\sqrt{29}$ and solve the Pell equation:  $x^2-29y^2=1$. 

\item Show that there are no rational points on the circle $x^2+y^2=3$.

\item Show that if $(x,y,z)$ is a primitive Pythagorean triple, then either $x$ or $y$ is divisible by $3$. 

\item Find all solutions in positive integers of the diophantine equation $x^2+2y^2=z^2$. 

\item Find all rational points on the ellipse $x^2+3y^2=4$ by determine the intersection of a line with rational slope $t$ that goes through $(1,1)$ with this ellipse. 

\item Show that the diophantine equation $x^4-y^4=z^2$ has no solutions in nonzero integers using the method of infinite descent. 






\end{enumerate}

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