$N = pq$ where $p$ and $q$ are distinct primes. $ZN^*$ is all $x$ belonging to $ZN$ such that $gcd(x, N) = 1$.
How do I find if $ZN^*$ is closed under addition?
I believe $QR \times QR$ gives a $QR$. Is this correct? What about $QR \times QNR$ and vice versa? Any help or pointers in the right direction will be appreciated.