Let R be the equivalence relation defined on Z by x Ry if x ² = y ² (Mod5). Give a partition on Z with respect to R.

(you may use the following results:

2 = 0 (mod 5) r = 1 (mod 5) r = 4 (mod 5) if and only if if and only if if and only if x = 0 (mod 5), x = 1 (mod 5) or I x = 2 (mod 5) or x = 4 (mod 5), x = 3 (mod 5). )