document.write( "Question 1059605: Prove that if 1 is added to the product of any four
\n" ); document.write( "consecutive integers, the sum is a perfect square.
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Algebra.Com's Answer #674661 by KMST(5328) $\"\"$ $\"About$

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Let the four consecutive integers be defined based on their avetshe, $\"a\"$ , as
\n" ); document.write( " $\"a-3%2F2\"$ , $\"a-1%2F2\"$ , $\"a%2B2%2F2\"$ , and $\"a%2B3%2F2\"$ .
\n" ); document.write( "The sum the problem talks about is
\n" ); document.write( " $\"%28a-3%2F2%29%28a-1%2F2%29%28a%2B1%2F2%29%28a%2B3%2F2%29%2B1\"$ =
\n" ); document.write( " $\"%28a%5E2-9%2F4%29%28a%5E2-1%2F4%29%2B1\"$ =
\n" ); document.write( " $\"a%5E4-%2810%2F4%29a%5E2%2B9%2F16%2B1\"$ =
\n" ); document.write( " $\"a%5E4-2%285%2F4%29a%5E2%2B25%2F16\"$ =
\n" ); document.write( " $\"%28a%5E2-5%2F4%29%5E2\"$ .
\n" ); document.write( " $\"a%5E2-5%2F4\"$ is an integer.
\n" ); document.write( "In fact, it is
\n" ); document.write( "the sum of $\"1\"$ plus the product if the first and fourth integers:
\n" ); document.write( " $\"1%2B%28a-3%2F2%29%28a%2B3%2F2%29=4%2F4%2Ba%5E2-9%2F4=a%5E2-5%2F4\"$ . \n" ); document.write( "

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