Is there a general concept for the congruence of a congruence?
Suppose we have three arbitrary integers $N, m$ and $n$. My question is whether $(N \bmod n) \bmod m$ corresponds to any known mathematical concept (beyond a double operation).
A simpler case, for $m=2$, would be: Is $N \bmod n$ even or odd? Is there any result for this kind of operation?