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

Question 548923: prove that product of 4 consecutive numbers cannot be the square of an integer
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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

If x = 0, then n^2 can be zero. o/w,
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To be a square,

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

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