Chinese remainder theorem

The chinese remainder theorem is a theorem from number theory. It is about congruence. The original form was:
The theorem says that there will be a solution to this question if there's no common factor between the row sizes. Using the original example, that is that no number divides both 3 and 7, both 3 and 5, nor both 5 and 7 (except, of course, 1). They're all coprime.
The Chinese remainder theorem is used in cryptography. For example, for the RSA algorithm.