document.write( "Question 1100005: 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
\n" ); document.write( "\n" ); document.write( "Prove that the product of any three consecutive integers is divisible by 6.\r
\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. \n" ); document.write( "

Algebra.Com's Answer #803146 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hello, it is really SIMPLE statement, and you do not need to use heavy artillery as that referred theorem.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This statement is for those BEGINNERS who solve their first problems on divisibility numbers\r
\n" ); document.write( "\n" ); document.write( "and make their first steps in learning this subject.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Trace attentively my reasons below.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    Of any three consecutive integer numbers, at least one is an EVEN number (divisible by 2)\r\n" );
document.write( "    and exactly one is divisible by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    These are self-evident facts.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Hence, the product of any three consecutive integer numbers is divisible by 2*3 = 6.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved, proved, explained and completed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For your education, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Introductory problems on divisibility of integer numbers\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is written specially for those BEGINNERS like you . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "By the way, at the end of that lesson, you will find numerous links to other lessons on divisibility numbers.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So, you have this happy opportunity to read about the subject in English.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is really a fascinating reading (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );