document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100005>Question 1100005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm really sorry, I don't study maths in English so I really have no idea where to put this one but please give it a try.\r<BR>\n" );
document.write( "\n" );
document.write( "Prove that the product of any three consecutive integers is divisible by 6.\r<BR>\n" );
document.write( "\n" );
document.write( "I have discovered that this could be solved with the Erdos�Ginzburg�Ziv theorem but unfortanetly I can't use that one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803110 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> integers: (n - 1)(n)(n + 1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There will be 1 odd, 2 even numbers or 2 odd, 1 even number, so the product is divisible by 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here are the possible remainders when the number is divided by 3:<BR>\n" );
document.write( "0, 1, 2<BR>\n" );
document.write( "1, 2, 0<BR>\n" );
document.write( "2, 0, 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There will always be at least one multiple of 3 in the product, so overall, the product is divisible by 6. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );