Help with math problem involving roots of a modulo operation?

Question: if x doesn’t divide N, what does “N (mod N/x)” mean?

@ratboy As an example of what it means, image a clock with 11.5 hours on it. It skips from eleven to zero faster than it should normally. Hours 1 – 11 will remain unchanged in mod 11.5, but 12 would cycle around and become 12 – 11.5 = 0.5. 50 will become 50 – 11.5 – 11.5 – 11.5 – 11.5 = 4.

Usually n (mod m) is considered non-negative, so that the sum could be 0 only if each of the summands were 0. Specifically: for integers n and m, n (mod m) = r iff for n = qm + r for some q and r where 0 <= r < N. It’s not trivial to extend the definition to real numbers since given any two non-zero real numbers, each divides the other evenly.