document.write( "Question 1059605: Prove that if 1 is added to the product of any four
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Algebra.Com's Answer #674657 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Prove that if 1 is added to the product of any four
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document.write( "The problem asks us to prove that n*(n+1)*(n+2)*(n+3) + 1 is a square of an integer.\r\n" );
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document.write( "Let x =  be the central point for the original four integers n, n+1, n+2 and n+3.  Then\r\n" );
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document.write( "  n*(n+1)*(n+2)*(n+3) + 1 = (x+0.5)*(x-0.5)*(x+1.5)*(x-1.5) + 1 = \r\n" );
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document.write( "=  =  = \r\n" );
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document.write( "=  = .\r\n" );
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document.write( "Next,   = (by the definition of \"x\") =  =   is the integer number.\r\n" );
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document.write( "Thus we proved that  n*(n+1)*(n+2)*(n+3) + 1  is the square of the integer number   = .\r\n" );
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