Linked from

The 30 pages that link to Chinese remainder theorem, each with the reason it gives.

• Modular arithmeticRelated: It reconstructs a residue modulo a product from compatible residues modulo smaller integers.

• Number theoryRelated: It explains when separate remainder constraints combine into a single integer residue class.

• Euclidean algorithmRelated: Combining congruences often requires inverses computed with the extended algorithm.

• Congruence (number theory)Related: It combines separate congruence conditions into a single solution.

• Coprime integersRelated: Coprime moduli guarantee a unique solution modulo their product.

• Euler's totient functionRelated: It gives a structural reason that φ(mn) = φ(m)φ(n) for coprime m and n.

• Cyclic groupRelated: It decomposes finite cyclic groups whose orders are products of coprime factors.

• Quotient ringRelated: It decomposes quotients by suitable product ideals into simpler rings.

• Chinese mathematicsBroader topic: A problem in the Nine Chapters gives an early form of this method.

• Composite numberRelated: Factoring a composite modulus lets computations split into smaller modular problems.

• RSA cryptosystemRelated: RSA implementations use it to speed private-key operations by working modulo each prime.

• Disquisitiones ArithmeticaeRelated: It exemplifies how congruences let Gauss combine separate modular conditions into one.

• Quadratic residueRelated: It reduces residue questions for composite moduli to questions at coprime factors.

• Modular exponentiationRelated: It can split a modular power into smaller computations when the modulus factors into coprimes.

• Bézout's identityRelated: Bézout coefficients help construct solutions when combining congruences with coprime moduli.

• Factor theoremCompared with: Despite the shared word theorem, it concerns modular arithmetic rather than polynomial factors.

• Least common multipleRelated: Its solutions repeat modulo the product, which is the least common multiple for coprime moduli.

• The Nine Chapters on the Mathematical ArtBroader topic: A problem in the text asks for a number with specified remainders, an early form of this problem.

• Finite cyclic groupRelated: It decomposes cyclic groups whose order factors into coprime components.

• Horner's methodRelated: Horner's name also became attached to a distinct Chinese remainder algorithm.

• Liu HuiCompared with: Its later prominence illustrates another mathematical development, not a direct result of Liu Hui’s work.

• Yang HuiRelated: It exemplifies the modular arithmetic problems treated in the Chinese mathematical tradition Yang Hui inherited.

• Hensel's lemmaCompared with: It combines solutions across distinct prime powers rather than lifting one solution along powers of a single prime.

• Wilson's theoremRelated: It can analyze the factorial congruence by separating a composite modulus into coprime factors.

• Qin JiushaoRelated: It names the class of problems Qin’s systematic method solves.

• Extended Euclidean algorithmRelated: Its constructive proofs use modular inverses obtainable from Bézout coefficients.

• Jia XianRelated: It represents the broader tradition of sophisticated algorithmic arithmetic in which Jia Xian worked.

• Zu ChongzhiRelated: Modular arithmetic offers a mathematical framework for reconciling recurring cycles in calendar computation.

• Zhu ShijieRelated: Earlier Chinese work on arithmetic congruences forms part of the mathematical heritage surrounding Zhu.

• Lucas's theoremCompared with: It combines modular answers across moduli, whereas Lucas's theorem computes within one prime modulus.