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