document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984151>Question 984151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would appreciate your help!\r<BR>\n" );
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document.write( "If k stands for an integer, then is it possible for k^2+k to stand for an odd integer? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604936 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If k stands for an integer, then is it possible for k^2+k to stand for an odd integer? Explain.\r<BR>\n" );
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document.write( "The answer is \"NO\".<BR>\n" );
document.write( "Case 1: k is an odd integer<BR>\n" );
document.write( "For some integer p, k = 2p + 1<BR>\n" );
document.write( "So, k + 1 = 2p + 2 = 2(p+1) = 2q for some integer q<BR>\n" );
document.write( "k^2 + k = k(k+1) = k(2q) = 2kq = 2r for some integer r.[Integers are closed under multiplication]<BR>\n" );
document.write( "Therefore, if k is an odd integer, then k^2 + k is an even integer\r<BR>\n" );
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document.write( "case 2: k is an even integer<BR>\n" );
document.write( "For some integer p, k = 2p<BR>\n" );
document.write( "So, k + 1 = 2p + 1 <BR>\n" );
document.write( "k^2 + k = k(k+1) = 2p(2p+1) , multiple of 2<BR>\n" );
document.write( "Therefore, if k is an even integer, then k^2 + k is an even integer </SPAN>\n" );
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