I've wondered why each multiplicative group I tested has modulo n either 1 or -1. Is there a rule?
For example:
$$\mathbb Z_{10}^*=\{1,3,7,9\}\\
1\cdot3\cdot7\cdot9=-1 \:(mod\:n)$$
or
$$\mathbb Z_{15}^*=\{ 1, 2, 4, 7, 8, 11, 13, 14 \}\\
1\cdot2\cdot4\cdot7\cdot8\cdot11\cdot13\cdot14=1 \:(mod\:n)$$
or
$$\mathbb Z_{5}^*=\{1,2,3,4\}\\
1\cdot2\cdot3\cdot4=-1 \:(mod\:n)$$
