This question may end up [closed], but I'm going to ask and let the people decide. It's certainly the kind of question that I'd ask people at tea, and it's not one whose answer I've been able find with Google.
TeX, I have heard, is Turing complete. In theory, this means that we can do modular arithmetic with LaTeX programs. I'd like to know how this can be done in practice.
Background: I've been using the \foreach command in TikZ to draw NxN arrays of nodes, indexed by pairs of integers (m,n). I'd like to be able to use modular arithmetic and an ifthenelse statement to put different decorations on the nodes, depending on the value of (m+n) mod p. Obviously, one can just do this by hand. But that's not the world I want to live in.