x and y must be positive, negative or 0, but because $x^{2013}+y^{2013}>x^{2012}+y^{2012}$, both of them cannot be 0 or 1 because 0 = 0 and 1=1. we should treat positive and negative x's and y's as the same because a positive number squared is equal to its opposite squared, so a^n+1 is more than a^n, so if $x^{2013}+y^{2013}>x^{2012}+y^{2012}$, then $x^{2014}+y^{2014}>x^{2013}+y^{2013}$ is true

$$(x^{2014}+y^{2014})(x^{2012}+y^{2012})\geq (x^{2013}+y^{2013})^2$$