最后更新于3年前
\left\{ \begin{array}{**lr**} x\equiv b_1\left(\mod m_1\right) &\\ \vdots &\\ x\equiv b_k\left(\mod m_k\right) \end{array} \right.
令m=m1⋅m2⋯mk=mi⋅Mim=m_1\cdot m_2\cdots m_k=m_i\cdot M_im=m1⋅m2⋯mk=mi⋅Mi Mi′⋅Mi≡1(mod mi),i=1,⋯ ,kM_{i}^{\prime}\cdot M_i\equiv1\left(\mod m_i\right), i=1,\cdots,kMi′⋅Mi≡1(modmi),i=1,⋯,k x≡∑i=1kbi⋅Mi′⋅Mi(mod m)x\equiv \sum\limits_{i=1}^{k}{b_i\cdot M_{i}^{\prime}\cdot M_i}\left(\mod m\right)x≡i=1∑kbi⋅Mi′⋅Mi(modm)