We prove that the cyclic inequality $\sum\limits_{i=1}^{i=n}\left(\frac{x_i}{x_{i+1}}\right)^k\geq\sum\limits_{i=1}^{i=n}\frac{x_i}{x_{σ(i)}}$ holds for $k$ in a specific range dependant on the permutation $σ$. We also show that the same is not true for the Sahpiro-type generalizations.
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