Prove that the equation ax ay (mod n) implies x y (mod n) whenever gcd

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Prove that the equation ax ≡ ay (mod n) implies x ≡ y (mod n) whenever gcd (a, n) = 1. Show that the condition gcd (a, n) = 1 is necessary by supplying a counterexample with gcd (a, n) > 1.

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