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Corollary 33.29

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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