Suppose I have three statements of congruence:
x = a mod n, y = b mod m, z = c mod p;
Furthermore, x is a given percent of x + y + z, as is y and z.
Does this uniquely determine x, y, z? Or does it at least restrict x to a predictable subset of the congruence class of a, and so on?
Thank you.
You need to put down all the equations and unknowns.
$ x= a +kn$, $ y= b +k'm$, $ z= c +k''p$, $ x= \alpha (x+y+z)$, $ y= \beta (x+y+z)$, $ z= \gamma (x+y+z)$.
I count 6 equations and 6 unknowns so there is a chance that there is a unique solution, but as you're working with integers, there might be no solutions.