Moreover,
is uniquely determined modulo . An equivalent statement is that if , then every pair of residue
classes modulo and corresponds to a simple residue
class modulo .

The Chinese remainder theorem is implemented in the Wolfram Language as ChineseRemainder[a1,
a2, ...m1,
m2, ...].
The Chinese remainder theorem is also implemented indirectly using Reduce
in with a domain specification of Integers.

The theorem can also be generalized as follows. Given a set of simultaneous congruences