document.write( "Question 1129671: Prove that the values of the polynomial x^3–x are divisible by 6 for whole values of x. \n" ); document.write( "

Algebra.Com's Answer #746235 by ikleyn(52878) $\"\"$ $\"About$

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document.write( "x^3 - x = x*(x-1)*(x+1),\r\n" );
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document.write( "so the left side is the product of three consecutive integer numbers.\r\n" );
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document.write( "Of them, at least one is a multiple of 2 and exactly one is a multiple of 3.\r\n" );
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document.write( "Hence, the product, which is x^3 - x, is divisible by 2*3 = 6.\r\n" );
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