Chinese remainder theorem

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Let m1, m2,…, mr be positive integers that are relatively prime to one another, and let their product be m: m = m1m2mr Let n, u1, u2,…, ur be integers; then there is exactly one integer, u, that satisfies nu < (m + n) and uuj (modulo mj) for 1 ≤ jr

m1, m2,…, mr

m = m1m2mr

nu < (m + n)

uuj (modulo mj) for 1 ≤ jr

Subjects: Computing.

Reference entries