Prove that for all n (elements of N) and a (elements of Z), the following

I

Ike Humminspurts

New member
statements are equivalent? Note: N = Natural Numbers, Z = Integers, Zn = Integers Modulo n

(i) gcd(a,n) = 1.
(ii) [a] has a multiplicative inverse in Zn.
(iii) The function g: Zn --> Zn defined by g([x]) = [ax] is injective.

Any help appreciated,

Thanks!
 
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