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Discuss the relation of congruence modulo

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Reference no: EM131578141

Question: The relation of "congruence modulo n" is the relation ≡ defined by x ≡ y mod n if and only if x mod n = y mod n.

(a) Show that congruence modulo n is an equivalence relation by showing that it defines a partition of the integers into equivalence classes.

(b) Show that congruence modulo n is an equivalence relation by showing that it is reflexive, symmetric, and transitive.

(c) Express the Chinese Remainder theorem in the notation of congruence modulo n.

Reference no: EM131578141

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