the congruence relation in z is
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We say that a, b ∈ Z are congruent modulo N if N|(a − b). We write a ≡ b mod N for “a is congruent to b modulo N.” [a]N := {b ∈ Z| b ≡ a mod N}. Note here that [a]N is the notation for this congruence class— in particular, [a]N stands for a subset of Z, not a number.
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