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Prove: Let n ∈ N, a ∈ Z, and gcd(a,n) = 1. For i,j ∈ N,...

Prove: Let n ∈ N, a ∈ Z, and gcd(a,n) = 1. For i,j ∈ N, aj ≡ ai (mod n) if and only if j ≡ i (mod ordn(a)). Where ordn(a) represents the order of a modulo n. Be sure to prove both the forward and backward direction.

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