If $x$ and $y$ are real numbers such that $x^{2013}+y^{2013}>x^{2012}+y^{2012}$, prove that $x^{2014}+y^{2014}>x^{2013}+y^{2013}$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013
Tags: algebra, inequalities
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013
Tags: algebra, inequalities
If $x$ and $y$ are real numbers such that $x^{2013}+y^{2013}>x^{2012}+y^{2012}$, prove that $x^{2014}+y^{2014}>x^{2013}+y^{2013}$