Theorems
Chinese Remainder Theorem
Also Known As Sunzi's Theorem
Number Theory
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The Chinese remainder theorem states that if the remainders of an integer's division by several pairwise coprime integers are known, the remainder of its division by the product of those integers can be uniquely determined. The earliest known special case appears in the Sunzi Suanjing, and Qin Jiushao gave the complete general solution in his 1247 treatise.
Facts
StatementGiven several pairwise coprime divisors and the remainder an integer leaves under each one, there is exactly one remainder that integer can leave under the product of all those divisors, and it is uniquely determined by the individual remainders. 1 Cross-Tradition Connections
Sources
1. Chinese Remainder Theorem (Wikipedia)
Wikimedia FoundationintroductionQuote, introduction
one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime
1. Chinese Remainder Theorem (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
Qin Jiushao provided a complete general solution in his 1247 work Mathematical Treatise in Nine Sections
Sunzi Suanjing (Wikipedia)
Wikimedia Foundationsignificance sectionQuote, significance section
Chapter 3 contains the earliest example of the Chinese remainder theorem, a key tool to understanding and resolving Diophantine equations.
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