structural:summarization
Uniqueness

Suppose that x and y are both solutions to all the congruences. As x and y give the same remainder, when divided by n, their difference x − y is a multiple of each n. As the n are pairwise coprime, their product N also divides x − y, and thus x and y are congruent modulo N. If x and y are supposed to be non-negative and less than N (as in the first statement of the theorem), then their difference may be a multiple of N only if x = y.