Y by megarnie, HamstPan38825, Rounak_iitr, Adventure10
Let
be positive reals, and let
. Prove that
Proposed by David Stoner

![$\sqrt[2013]{\frac{3}{a^{2013}+b^{2013}+c^{2013}}}=P$](http://latex.artofproblemsolving.com/7/4/c/74cf90a8ac449982b9bd5c82ab397e4ef5a519a9.png)
![\[\prod_{\text{cyc}}\left(\frac{(2P+\frac{1}{2a+b})(2P+\frac{1}{a+2b})}{(2P+\frac{1}{a+b+c})^2}\right)\ge \prod_{\text{cyc}}\left(\frac{(P+\frac{1}{4a+b+c})(P+\frac{1}{3b+3c})}{(P+\frac{1}{3a+2b+c})(P+\frac{1}{3a+b+2c})}\right).\]](http://latex.artofproblemsolving.com/a/1/d/a1d517f3135da85696d4d52b674fe759eb1bd3c2.png)
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