document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475377>Question 475377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let (a,b,c) be a primitive pythagorous triplet(a<b<c).show that c is odd. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326399 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By the Pythagorean theorem,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a^2 + b^2 = c^2\">\r<BR>\n" );
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document.write( "Assume c is even. Then c^2 &#8801; 0 (mod 4), and a^2 or b^2 can only be congruent to 0 or 1 mod 4, so this creates a contradiction (unless a,b,c are all divisible by 2, which still doesn't work since the triple is primitive). Hence, c must be odd. </SPAN>\n" );
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