# Question about proof

1. Sep 28, 2009

### koukou

prove Byron's Conjecture. Define the set
Znx={k∈Zn but not including zero ：gcd(k; n) = 1}
(a) Prove that Znx is a group under multiplication (mod n).
(b) Prove that an element a∈Zn is invertible in Zn (with respect to multiplication (mod n)) if and only if a∈Znx

Znx x should be above n . i dont know how to type

2. Oct 1, 2009

### jbunniii

What's the question?

3. Oct 1, 2009

### VeeEight

Use the fact that you can write out ak + bn = 1 for some integers a,b to show the elements are invertible.

4. Oct 2, 2009

### g_edgar

LaTeX: $\mathbb{Z}_n^{\times}$ ... use the "Quote" button to see it.