Let R be the equivalence relation on Z defined by xRy if x^2 ≡ y^2(mod 5). Give a partition on Z with respect to R.
(Hint: You may use the following results: For any x ∈ Z, x^2 ≡ 0 (mod 5) if and only if x ≡ 0 (mod 5), x^2 ≡ 1 (mod 5) if and only if x ≡ 1 (mod 5) or x ≡ 4 (mod 5), x^2 ≡ 4 (mod 5) if and only if x ≡ 2 (mod 5) or x ≡ 3 (mod 5). )