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A note on the determination of hyperbolic knots by their cyclic unbranched coverings

We show that, for any prime p, a hyperbolic knot K in S 3 is determined by its p-fold cyclic unbranched covering. We also investigate when the m-fold cyclic un-branched covering of a hyperbolic knot in S 3 coincides with the n-fold cyclic unbranched covering of another knot, for different coprime integers m and n.