While working on a menial task in front of a clock today I was distracting myself by proving that all three hands only align twice a day. That lead me to wonder how one would deal with more complex problems involving modulo arithmetic. I know several rules for reducing equations involving all sorts of operators from simple addation up through very complex triple integrals and the like. But, I never learned any rules for manipulating the mudulo operator.
What are valid oberations that can be used to reduce eautaions involving multiple modulo operators?