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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 a2. Then
1. (x-3)(x-1)(x+1)(x+3) = (x2 - 1)(x 2 - 9) = (x4 - 10x2 + 9) = a2.
2. By quadratic formula, x2 = 10 V/ 100-49-аг)

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!

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