SOLUTION: prove that product of 4 consecutive numbers cannot be the square of an integer

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Question 548923: prove that product of 4 consecutive numbers cannot be the square of an integer
Answer by Alan3354(69443) About Me  (Show Source):
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prove that product of 4 consecutive numbers cannot be the square of an integer
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(x-1)*x*(x+1)*(x+2) = n^2
x%2A%28x%5E3+%2B+2x%5E2+-+x+-+2%29+=+n%5E2
If x = 0, then n^2 can be zero. o/w,
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To be a square,
x%5E3+%2B+2x%5E2+-+2x+-+2+=+0
There are no integer solutions.
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It can be the square of an integer if one integer is zero, o/w not.
eg, 0*1*2*3 = 0^2
-1*0*1*2 = 0^2