Question: Let sim be the relation on mathbb{Z} Z defined by: xsim y x y if and only if (x^2-y) ( x 2 y ) is

Let \sim

be the relation on \mathbb{Z}

Z defined by:

"x\sim y

xy if and only if (x^2-y)

(x2

y) is even."

Prove that this relation is an equivalence relation, i.e., it is reflexive, symmetric, and transitive.

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