# Question about a proof in Junod's paper about the Blum-Blum-Shub generator

I am reading Junod's paper about the Blum-Blum-Shub generator. There is one thing I just do not understand about his proof of Lemma 4. On page 17 he writes:

We conclude that $$x=-x_0$$ and from Lemma 1 we know that $$x \ne x_0$$

(So far I understand.)

, so they must have different parities (Why is this the case?), $$n$$ beeing odd, which is a contradiction.

Could you please explain that to me?

If $$x_0$$ is odd, then $$-x_0 = n - x_0$$ must be even (and versa-visa).