document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924485>Question 924485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove algebraically that <BR>\n" );
document.write( "(2n+1)^2-(2n+1) is an even number\r<BR>\n" );
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document.write( "for all positive integer values of n.\r<BR>\n" );
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document.write( "Please help :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728792 by </B><A HREF=/tutors/aboutme.mpl?userid=amalm06><B>amalm06(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amalm06><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=amalm06><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose it's an odd number instead. That is, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n%2B1%29%5E2-%282n%2B1%29 ALIGN=MIDDLE  ALT=\"%282n%2B1%29%5E2-%282n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%2B1 ALIGN=MIDDLE  ALT=\"2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for some k&#8712;Z\r<BR>\n" );
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document.write( "On the other hand,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%5E2%2B4n%2B1-2n-1=4n%5E2%2B2n=2%282n%5E2%2Bn%29 ALIGN=MIDDLE  ALT=\"4n%5E2%2B4n%2B1-2n-1=4n%5E2%2B2n=2%282n%5E2%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is an even number. This contradicts the original hypothesis. \r<BR>\n" );
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