Question 548923
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*(x^3 + 2x^2 - x - 2) = n^2}}}
If x = 0, then n^2 can be zero.  o/w,
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To be a square,
{{{x^3 + 2x^2 - 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