Let $m_1$, $m_2$, ..., $m_k$ be pairwise relatively prime; $M=m_1m_2\cdots m_k$; $M_1=M/m_1$, $M_2=M/m_2$, ..., $M_k=M/m_k$; and $M_1y_1\equiv1(\text{mod }m_1)$, $M_2y_2\equiv1(\text{mod }m_2)$, ..., $M_ky_k\equiv1(\text{mod }m_k)$. How can I show that $M_1y_1+M_2y_2+\cdots+M_ky_k\equiv1(\text{mod }M)?$
Evaluating a Simple Congruence
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elementary-number-theory
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0This is the last step of a long theorem I am trying to prove. I just cannot seem to find a way. :/ – 2012-03-07