# Question: find the error in the proof statement there is no...

###### Question details

**Find the error in the proof.**

**Statement: There is no perfect square that is the
product of four consecutive odd integers. (Note: this is false as 9
= 3 ^{2} = (-3)*(-1)*(1)*(3) = 9)**

Proof: Assume to the contrary, that there exist four consecutive
odd integers x-3, x-1, x+1, and x+3 such that their product is
a^{2}. Then

1. (x-3)(x-1)(x+1)(x+3) = (x^{2} - 1)(x ^{2} - 9) =
(x^{4} - 10x^{2} + 9) = a^{2}.

2. By quadratic formula, x^{2} =

3. Since 4 is even, then x^2 = 5 + 4*sqrt(16+a^2) must be odd

4. It then follows that x is odd. However, this is a contradiction since our assumption states that (x-3),(x-1),(x+1),(x+3) are all odd integers.

Any help would be appreciated! Note: The statement is false so there is clearly an error in this proof. Thanks!