Public key in fully homomorphic encryption over the integers I'm reading “Fully Homomorphic Encryption over the Integers” by van Dijk et al.

I wonder why $x_0$, which is a component of the public key, should be an odd number?
(even number mod even number) is always even number and (odd number mod even number) is always odd number. If $m=0$, the result of modular $x_0$ will be always even number. If $m=1$, the result will be odd number. So $x_0$ should be a odd number.