document.write( "Question 1070276: Show that if n is odd integer, then n^3-n is a multiple of 24. \n" ); document.write( "

Algebra.Com's Answer #685404 by ikleyn(52781) $\"\"$ $\"About$

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document.write( " =  =  = .\r\n" );
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document.write( "You have a product of three consecutive integers. \r\n" );
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document.write( "One of them is a multiple of 3.\r\n" );
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document.write( "If n is odd, then both (n-1) and (n+1) are even, i.e. are multiples of 2.\r\n" );
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document.write( "Moreover, one of these two is a multiple of 4.\r\n" );
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document.write( "Therefore, the entire product is a multiple of 2*3*4 = 24.\r\n" );
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document.write( "QED.\r\n" );
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