|Keep It Simple, Stupid|
ps. why would I want to read a book on number theory to understand why a basic operator behaves the way it does?
The answer is "So you know what you are talking about". I admit I was too quick off the gun as well, however. After some further research I found that the modulo function was devised by Abel in the 1700's to allow him to study large and complicated groups with only pencil and paper.
Modulo is hardly a basic operator. It's just a basic operator for you because you've only ever used it in simple situations.
Computer implementations of functions are usually nasty bastardisations of real math functions. This is why the original poster mentioned Knuth, who did a lot of work involving math and computers.
Incidentally, 'proof by random web pages' is a poor way of proving that you are right.