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For every odd integer , we raise an example of a prime component-preservingly amphicheiral link with the minimal crossing number . The link has two components, and consists of an unknot and a knot which is -amphicheiral with odd minimal crossing number. We call the latter knot a {\it Stoimenow knot}. We also show that the Stoimenow knot is not invertible by the Alexander polynomials.

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