document.write( "Question 747469: For any positive integer 'n' prove that 'n3-n' is divisible by 6.
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Algebra.Com's Answer #456143 by tommyt3rd(5050) $\"\"$ $\"About$

You can put this solution on YOUR website!
not true:\r
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\n" ); document.write( "\n" ); document.write( "n^3-n=0\r
\n" ); document.write( "\n" ); document.write( "Maybe you mean if n is 2 or greater?\r
\n" ); document.write( "\n" ); document.write( " $\"%0D%0A%0D%0An%5E3-n=%28n%29%28n%5E2-1%29=%28n-1%29%28n%29%28n%2B1%29%0D%0A\"$ \r
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\n" ); document.write( "\n" ); document.write( "now for \r
\n" ); document.write( "\n" ); document.write( " $\"n%3E=2\"$ \r
\n" ); document.write( "\n" ); document.write( "this product will include 3 consecutive numbers and that means at least one of them will be even and exactly one will be a multiple of 3. Therefore each will be a multiple of 6.\r
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\n" ); document.write( "\n" ); document.write( ":) \n" ); document.write( "

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