Which of the following sets is a complete set of representatives modulo 7? Which of the following sets is a complete set of representatives modulo 7?
1) (1, 8, 27, 64, 125, 216, 343)
1 mod 7 = 1
8 mod 7 = 1
27 mod 7 = 6
64 mod 7 = 1
125 mod 7 = 6
216 mod = 6
343 mod = 0
2) (1, -3, 9, -27, 81, -243, 0)
1 mod 7 = 1
-3 mod 7 = 4
9 mod 7 = 2
-27 mod 7 = 1
81 mod 7 = 4
-243 mod 7 = 2
0 mod 7 = 0
3) (0, 1, -2, 4, -8, 16, -32)
0 mod 7 = 0
1 mod 7 = 1
-2 mod 7 = 5
4 mod 7 = 4
-8 mod 7 = 6
16 mod 7 = 2
-32 mod 7 = 3
i think its only 1. but wanted to make sure.

$3)~~ (0, 1, -2, 4, -8, 16, -32)$ is only complete set of $\pmod 7$.
$$0 \pmod 7 = 0$$
$$1 \pmod 7 = 1$$
$$-2 \pmod 7 = 5$$
$$4 \pmod 7 = 4$$
$$-8 \pmod 7 = 6$$
$$16 \pmod 7 = 2$$
$$-32 \pmod 7 = 3$$
they all have a unique solution from $0$ to $6$.
