Let and be Positive Integers which are Relatively Prime and let and be any two
Integers. Then there is an Integer such that

(1) |

(2) |

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

(3) |

(4) |

(5) |

(6) |

**References**

Ireland, K. and Rosen, M. ``The Chinese Remainder Theorem.'' §3.4 in
*A Classical Introduction to Modern Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 34-38, 1990.

Uspensky, J. V. and Heaslet, M. A. *Elementary Number Theory.* New York: McGraw-Hill, pp. 189-191, 1939.

Wagon, S. ``The Chinese Remainder Theorem.'' §8.4 in *Mathematica in Action.*
New York: W. H. Freeman, pp. 260-263, 1991.

© 1996-9

1999-05-26