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Chinese remainder theorem

For pairwise coprime positive integers

m_{1}, \dots, m_{r}

, reduction induces a ring isomorphism

Z / (m_{1} \dots m_{r}) Z ≅ \prod_{j = 1}^{r} Z / m_{j} Z .

Equivalently, every list of residue classes modulo the

m_{j}

has a unique simultaneous residue class modulo their product.

Table of contents 120 3
- Lagrange theorem for polynomial congruences Chinese remainder theorem 46
- Chinese remainder theorem for unit groups Chinese remainder theorem 36 1
  - Multiplicative order under the Chinese remainder theorem Chinese remainder theorem for unit groups 22

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