document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=769172>Question 769172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this question: show that 4  does not divide (n^2+2) for any n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468735 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Need to show that (n^2 + 2)/4 is not an integer<BR>\n" );
document.write( "For n odd, n^2 is always odd -> n^2 + 2 is always odd.  An odd number does not divide evenly by 4.<BR>\n" );
document.write( "(n^2 + 2)/4 = n^2/4 + 1/2<BR>\n" );
document.write( "For n even, n^2/4 will always give an integer value<BR>\n" );
document.write( "This is because an even number can be written as a multiple of 2, i.e. 2k<BR>\n" );
document.write( "n^2/4 = 4k^2/4 = k^2 = integer for all values of k<BR>\n" );
document.write( "An integer + 1/2 is not a whole number, so it does not divide evenly for even values of n<BR>\n" );
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