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	<title>blog.brightstartutors.com &#187; Number Theory</title>
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	<link>http://brightstartutors.com/blog</link>
	<description>mathematics and physics - learning and enjoying</description>
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		<title>Finding Formulas by Guessing</title>
		<link>http://brightstartutors.com/blog/2011/10/05/formulasbyguessing/</link>
		<comments>http://brightstartutors.com/blog/2011/10/05/formulasbyguessing/#comments</comments>
		<pubDate>Wed, 05 Oct 2011 06:31:39 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Computers and Mathematics]]></category>
		<category><![CDATA[Number Theory]]></category>
		<category><![CDATA[Problem Solving Techniques]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=1594</guid>
		<description><![CDATA[In my high school library, there was a copy of the classic book "Men of Mathematics" by E.T. Bell. Each chapter is a short biography of a notable mathematician of the past (and yes, they are all men). In the chapter on Carl Friedrich Gauss (1777-1855), I first encountered the famous story of how, as a 10 year old student, Gauss baffled his teacher by instantly solving a problem that the teacher assumed would occupy his student's an hour or more.

In this post, I will describe Gauss' insight, then show how a related problem can be solved by using some informed guesswork.]]></description>
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		<title>The Basel Problem</title>
		<link>http://brightstartutors.com/blog/2010/09/29/baselproblem/</link>
		<comments>http://brightstartutors.com/blog/2010/09/29/baselproblem/#comments</comments>
		<pubDate>Wed, 29 Sep 2010 17:12:11 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Euler's Greatest Hits]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=779</guid>
		<description><![CDATA[The history of mathematics has many instances where someone has posed a problem for the mathematical world at large to solve, and the problem was not resolved for decades, or even centuries. Often, new mathematics has been discovered in the process of working out a solution.
This post is the story of one such case, the so-called Basel Problem, first posed as a challenge to European mathematicians in 1644. It withstood all attempts to solve it until, in 1734, young Leonard Euler found the answer. As the reader will see, Euler's solution is a work of astonishing ingenuity, even though the level of the mathematics does not go beyond Algebra I.]]></description>
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		<slash:comments>4</slash:comments>
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		<title>Pythagorean Triples</title>
		<link>http://brightstartutors.com/blog/2010/07/21/pythagorean-triples/</link>
		<comments>http://brightstartutors.com/blog/2010/07/21/pythagorean-triples/#comments</comments>
		<pubDate>Wed, 21 Jul 2010 17:30:54 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Learning Math]]></category>
		<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/?p=650</guid>
		<description><![CDATA[
When math textbooks need an example of a right triangle, they frequently use a triangle with sides of length 3, 4, and 5, since the numbers work out so nicely: \(3^{2}+4^{2}=5^{2}\) by the Pythagorean theorem. If that gets tiresome, 12, 5, 13 might be used: \(5^{2}+12^{2}=13^{2}\). Clearly, multiplies of these numbers work also, e.g. \(6^{2}+8^{2}=10^{2}\).
Such [...]]]></description>
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		<slash:comments>0</slash:comments>
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		<title>How Many Prime Numbers Are There?</title>
		<link>http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/</link>
		<comments>http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/#comments</comments>
		<pubDate>Wed, 25 Nov 2009 00:59:36 +0000</pubDate>
		<dc:creator>curiousCharacter</dc:creator>
				<category><![CDATA[Mathematics History]]></category>
		<category><![CDATA[Number Theory]]></category>
		<category><![CDATA[Thrilling Math]]></category>

		<guid isPermaLink="false">http://brightstartutors.com/blog/2009/11/24/how-many-prime-numbers-are-there/</guid>
		<description><![CDATA[Are there an infinite number of prime numbers? Or maybe there is a largest prime number, and every number after that is composite. To get a little insight into this, we might start listing the prime numbers, beginning 2, 3, 5, 7, 11, …,  to see if any pattern emerges. About all that is [...]]]></description>
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