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Let Zn = {0, 1, 2, . . . , n − 1}, let · represent...

Let Zn = {0, 1, 2, . . . , n − 1}, let · represent multiplication (mod n), and let a ∈ Zn. Prove that there exists b ∈ Zn such that a · b = 1 if and only if gcd(a, n) = 1.

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