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Corollary 31.29

If \(n_1, \; n_2, \; \cdots \; n_k\) are pairwise relatively prime and \(n \;=\; n_1 n_2 \cdots \; n_k\), then for all integers x and a, \(x \; \equiv \;a\; {\rm mod} \; n_i\) iff \(x \; \equiv \;a\; {\rm mod} \; n\).


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