Statement of Chinese Remainder Theorem
Theorem states that a system of simultaneous congruences, defined by pairwise coprime positive integers (n1, n2,…., nk ) and arbitrary integers (a1, a2,…., ak )
x ≡ a1 (mod n1)
x ≡ a2 (mod n2)
⦙
x ≡ ak (mod nk)
has a unique solution modulo (N = n1 n2 …. nk)
Chinese Remainder Theorem
Chinese Remainder Theorem is a mathematical principle that solves systems of modular equations by finding a unique solution from the remainder of the division. It is used in cryptography and computer science for efficient computation.
In this article, we will learn the meaning and definition of the Chinese Remainder Theorem, the history of the Chinese Remainder Theorem, the statement and proof of the Chinese Remainder Theorem and applications of the Chinese Remainder Theorem.
Table of Content
- What is The Chinese Statement Theorem?
- History of Sun Zi
- Statement of Chinese Remainder Theorem
- Chinese Remainder Theorem Proof
- Application of the Chinese Remainder Theorem