FTP, name this theorem from number theory that states that a unique solution exists for a system of simultaneous congruences with pairwise coprime moduli and that is named for its Asian country of origin.
Proof of the elementary form of this result hinges on an argument that, by hypothesis, the greatest common divisor of the moduli of two congruences divides the difference of the bases of those congruences.  That elementary form, may be easily generalized to an arbitrary system of congruences in certain cases. The earliest known use of this lemma is in the solution to Problem 26 of the Sun Tsu Suan Chang, in which the moduli of a set of three congruences are prime and, therefore, coprime, as this theorem requires. FTP, name this theorem from number theory that states that a unique solution exists for a system of simultaneous congruences with pairwise coprime moduli and that is named for its Asian country of origin.
Proof of the elementary form of this result hinges on an argument that, by hypothesis, the greatest common divisor of the moduli of two congruences divides the difference of the bases of those congruences.  
Chinese remainder theorem