Chinese Remainder Theorem

GRE Math Subject · Axiom Academy

LESSON Chinese Remainder Theorem Solving systems of congruences and decomposing modular arithmetic Chinese Remainder Theorem (CRT) Existence: A solution always exists when the moduli are pairwise coprime Uniqueness: The solution is unique modulo the product The ring isomorphism form of CRT has powerful consequences that appear on the GRE: Yes! Since are pairwise coprime, CRT gives . Problem 1: Find the smallest positive integer satisfying and . Problem 2: How many solutions does have?

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