document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304084>Question 304084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give a counterexample: the square of a number added to the sum of twice the number and 8 is a prime number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217846 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=217846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pick any even number.<BR>\n" );
document.write( "Squaring it results in a number that has a factor of 2.<BR>\n" );
document.write( "Doubling it and adding 8 also results in a number that has a factor of 2.<BR>\n" );
document.write( "So the resulting sum will always have a factor of 2 as well.<BR>\n" );
document.write( "And thus cannot be prime.\r<BR>\n" );
document.write( "\n" );
document.write( "So pick 2 or 4 or any even number.<BR>\n" );
document.write( "And you will have your counter example<BR>\n" );
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