Define the relation τ on Z by aτ b if and only if there exists x ∈ {1,4,16} such that
ax ≡ b (mod 63).
(a) Prove that τ is an equivalence relation.
(b) Prove that there exists an integer n with 1 ≤ n ≤ 62 such that the equivalence class of n is{m ∈ Z | m ≡ n (mod 63)}.
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