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## Homework Statement

Consider the group {G, Xn} where

G is the set containing the n - 1 residue

classes modulo n excluding 0.

Which members are generators of {G, Xn} when

n = 7?

## The Attempt at a Solution

The right answers are 3 and 5.

I get 2 only.

My table of results

[tex]1: 1^1 = 1[/tex]

[tex]2: 2^1 = 2, 2^2 = 4, 2^3 = 4, 2^4 = 2[/tex]

[tex]3: 3^1 =3, 3^2 = 2, 3^3 = 4[/tex]

[tex]4: 4^1 =4, 4^2 = 2[/tex]

[tex]5: 5^1 = 5, 5^2 =4[/tex]

[tex]6: 6^1 = 6, 6^2 = 1[/tex]

[tex]7: 7^1 = 7, 7^2 = 7[/tex]