Chinese remainder theorem

The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published some time between the 3rd and 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. In Sun Tzu's example (stated in modern terminology), what is the smallest 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?