CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search The Chinese remainder theorem was proved by Gauss with his 1801 book Disquisitiones Arithmeticae . [ 1 ] The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra . It was first published in the 3rd to 5th centuries by the Chinese mathematician Sun Tzu . In its basic form, the Chinese remainder theorem will determine a number n that, when divided by some given divisors, leaves given remainders. For example, what is the lowest number n that when divided by 3 leaves a remainder of 2, when divided by 5 leaves a remainder of 3, and when divided by 7 leaves a remainder of 2? 1 Theorem statement 2 Existence and uniqueness 2.1 Case of two equations ( k = 2 ) 2.2 General case 3 Finding the solution with basic algebra ...