What is the proof for Byron's Conjecture? Define Znx and prove its properties.

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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 don't know how to type
 
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Use the fact that you can write out ak + bn = 1 for some integers a,b to show the elements are invertible.
 
LaTeX: \mathbb{Z}_n^{\times} ... use the "Quote" button to see it.
 

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