The answers to exercises marked IBB] can be found in the Back of the Book.
For a, b ∈ Z, define a ~ b if and only if a2 − b2 is divisible by 3.
(a) [BB] Prove that ~ defines an equivalence relation on Z.
(b) What is 0? What is I?
(c) What is the partition of Z determined by this equivalence relation?
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