Chinese Remainder Theorem
Computer Science
About Chinese Remainder Theorem
Combine two remainder patterns, construct their shared residue class, and see when common factors make the conditions compatible or impossible.
A number can leave different remainders when divided by different moduli. Can those observations identify the number? The Chinese Remainder Theorem combines congruences into one residue class. For coprime moduli, every pair of remainders has a solution, unique modulo their product. Sharing a factor changes the question: some pairs agree, while others contradict each other. NIST DLMF, section 27.15 states the coprime theorem.
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