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Define a relation on the integers by x y if x 2 y 2 is a multiple of 5. (a) Show that

Define a relation on the integers by x ∼ y if x2 − y2 is a multiple of 5.

(a) Show that ∼ is an equivalence relation.

(b) How many equivalence classes does ∼ have? Explain your reasoning.

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