document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228349>Question 228349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does anyone know what Pythagorean triples are and a set of formulas that will generate an infinite number of them.  I am so lost and can't figure this out for anything.  can someone explain this to me please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169540 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=169540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Check out the following hyperlink.  It's the most direct and to the point reference I could find.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.math.uic.edu/~fields/puzzle/triples.html\" target = \"_blank\">Pythagoren Triples</a>\r<BR>\n" );
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document.write( "This set of formulas should do the trick.\r<BR>\n" );
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document.write( "Here's a copy of what's on that website.\r<BR>\n" );
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document.write( "There is a simple formula that gives all the Pythagorean triples. <BR>\n" );
document.write( "Suppose that m and n are two positive integers, with m < n. Then n2 - m2, 2mn, and n2 + m2 is a Pythagorean triple. \r<BR>\n" );
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document.write( "Given any two numbers, m and n, with m < n, you can generate a set of pythagorean triples from it.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "3,4\r<BR>\n" );
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document.write( "first number is n^2 - m^2 = 16 - 9 = 7<BR>\n" );
document.write( "second number is 2mn = 2*3*4 = 24<BR>\n" );
document.write( "third number is n^2 + m^2 = 9 + 16 = 25\r<BR>\n" );
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document.write( "should  be a reight triangle with f^2 + s^2 = t^2\r<BR>\n" );
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document.write( "7^2 = 49<BR>\n" );
document.write( "24^2 = 576<BR>\n" );
document.write( "25^2 = 625\r<BR>\n" );
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document.write( "49 + 576 = 625\r<BR>\n" );
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document.write( "seems to work.\r<BR>\n" );
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document.write( "try m = 1 and n = 2\r<BR>\n" );
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document.write( "f (first) = 2^2 - 1^2 = 4-1 = 3<BR>\n" );
document.write( "s (second) = 2mn = 2*1*2 = 4<BR>\n" );
document.write( "t (third) = 2^2 + 1^21 = 4+1 = 5\r<BR>\n" );
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document.write( "not too shabby.\r<BR>\n" );
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document.write( "try 5 and 7\r<BR>\n" );
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document.write( "f = 7^2 - 5^2 = 49 - 25 = 24<BR>\n" );
document.write( "s = 2*5*7 = 10*7 = 70<BR>\n" );
document.write( "t = 7^2 + 5^2 = 49 + 25 = 74\r<BR>\n" );
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document.write( "24^2 + 70^2 = 74^2 becomes:<BR>\n" );
document.write( "576 + 4900 = 5476 becomes:<BR>\n" );
document.write( "5476 = 5476\r<BR>\n" );
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document.write( "It works !!!!\r<BR>\n" );
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document.write( "A pythagorean triple is a set of integers that forms a right triangle.   \r<BR>\n" );
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document.write( "This formula appears to work in all cases.\r<BR>\n" );
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document.write( "Here is a much more complicated explanation which winds up with the same formula stated above.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://mathforum.org/dr.math/faq/faq.pythag.triples.html\" target = \"_blank\">Pythagorean Triples Formuls and Examples</a>\r<BR>\n" );
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document.write( "Here's a definition.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathopenref.com/pythagoreantriples.html\" target = \"_blank\">Definition of Pythagorean Triple</a>\r<BR>\n" );
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document.write( "the derivtion gets pretty complicated, but the basic formula as stated in the first hyperlink holds.\r<BR>\n" );
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document.write( "You can find lots more info by doing a search on the web for \"pythagorean triples\"\r<BR>\n" );
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document.write( " </SPAN>\n" );
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