# Thread: Prove that Un is a group with respect to multiplication.

1. ## Prove that Un is a group with respect to multiplication.

For an integer n > 1, let G = Un, the group of units in Zn; that is, the set of all [a] in Zn that have multiplicative inverses. Prove that Un is a group with respect to multiplication.

2. Originally Posted by MissMousey
For an integer n > 1, let G = Un, the group of units in Zn; that is, the set of all [a] in Zn that have multiplicative inverses. Prove that Un is a group with respect to multiplication.
Theorem: The equation $ax\equiv1\text{ mod }n$ is solvable precisely when $(a,n)=1$