document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965979>Question 965979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that the product of any three consecutive numbers is even. <BR>\n" );
document.write( "So far I have tried ,      (n)(n+1)(n+2)=n^3+3n^2+2n<BR>\n" );
document.write( "but there is no multiple of an even number. I'm not sure what kind of proof method it is but this would be a proof with the same method. i.e prove that the sum of three consecutive odd numbers is divisible by 3 ,       2n+1+2n+3+2n+5= 6n+9  3(2n+3)     is a multiple of three therefore it is divisible by three.\r<BR>\n" );
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document.write( "Any help would be appreciated, hope it is not too confusing <BR>\n" );
document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728798 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Even the product of any TWO consecutive integers is even integer.\r<BR>\n" );
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document.write( "See my proof under this link\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.924485.html>https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.924485.html</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.924485.html\r<BR>\n" );
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document.write( "It implies that the product of any THREE consecutive integers is even number, too.\r<BR>\n" );
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