This is the kind of arithmetic I like.
Chico in The Magnificent Seven
When I was a student I was not particularly impressed with modular arithmetic. Initially, to me, it seemed like an abstract toy to play with. It didn’t look as though it was useful or deep. Now I fully appreciate it as I have seen it used repeatedly, and widely, in real-life applications such as cryptography (which includes internet security), data storage, bar-codes, ISBN details (on the backs of books) and even magic tricks.
The idea of modular ...