\item
Prove that the quadratic form $q(x) = x_1^2 + x_2^2 - p (x_3^2 + x_4^2)$
does not represent zero, when $p=3$ or more generally when $p$ is a prime
congruent to $3 \mod 4$.


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<h3> Topics in Geometry and Dynamics </h3>

<A HREF="pics/Horoballs.pdf">
<img src="pics/Horoball.pdf"> </A>

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<A HREF="http://isites.harvard.edu/icb/icb.do?keyword=k107775&login=yes">
<b> Math 275 - Harvard University </b>  </A>


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	<A HREF="syl.html"> Syllabus and references </A>

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<A HREF="home/notes/3manifolds.pdf">
	Notes on 3-manifolds! </A>

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<A HREF="home/course/course.pdf">
	Course notes </A>

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<A HREF="home/problems/problems.pdf">
	Problems </A>

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	Discussion Group:  Fridays, 12:30, 4th Floor Commons </A>

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<A HREF="hw.html">
	Homework Essays </A>

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<A HREF="http://math.harvard.edu/~ctm/home/text/others/bergelson/ergodic_theorem_history/ergodic_theorem_history.pdf">
	History of the ergodic theorem </A>

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<A HREF="http://math.harvard.edu/~ctm/home/text/others/newcomb/logs/logs.pdf">
	Frequency of different decimal digits </A>
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