y = x^(a^2 - 2a -3)

-y = (-x)^(a^2-2a-3)

x^(a^2-2a-3)=(-x)^(a^2-2a-3)=(- 1)^(a^2-2a-3)* x^(a^2-2a-3)

So when 2-2a-3 is an even number.

Let s = a 2-2a-3 = (a- 1)? -4

So when a is odd, a- 1 is even, (a- 1)? It's even, and s is even.

To sum up, when a is odd, the meaning of the problem is satisfied.