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Q: List the congruence classes mod 4 and show [1] + [3] = [0]. Classes: [0] = {..., -4, 0, 4, 8, ...}, [1] = {..., -3, 1, 5, ...}, [2] = {..., -2, 2, 6, ...}, [3] = {..., -1, 3, 7, ...}. [1]+[3]: pick 1+3 = 4 ∈ [0] ✓. (Any picks land in [0]!) ℤ/4ℤ = {[0],[1],[2],[3]} - arithmetic on 4 classes!