document.write( "Question 548923: prove that product of 4 consecutive numbers cannot be the square of an integer \n" ); document.write( "

Algebra.Com's Answer #357400 by Alan3354(69443) $\"\"$ $\"About$

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prove that product of 4 consecutive numbers cannot be the square of an integer
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\n" ); document.write( "(x-1)*x*(x+1)*(x+2) = n^2
\n" ); document.write( " $\"x%2A%28x%5E3+%2B+2x%5E2+-+x+-+2%29+=+n%5E2\"$
\n" ); document.write( "If x = 0, then n^2 can be zero. o/w,
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\n" ); document.write( "To be a square,
\n" ); document.write( " $\"x%5E3+%2B+2x%5E2+-+2x+-+2+=+0\"$
\n" ); document.write( "There are no integer solutions.
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\n" ); document.write( "It can be the square of an integer if one integer is zero, o/w not.
\n" ); document.write( "eg, 0*1*2*3 = 0^2
\n" ); document.write( "-1*0*1*2 = 0^2
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