Chinese Remainder Theorem
Notes
Suppose
![n_{1},...,n_{k}](http://latex.codecogs.com/gif.latex?n_{1},...,n_{k})
are positive integers that are pairwise coprime. Then, for any given sequence
of integers
![a_{1},...,a_{k}](http://latex.codecogs.com/gif.latex?a_{1},...,a_{k})
there exists an integer
x that solves the following system of simultaneous congruences:
A solution
x exists if and only if