Problem

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Tags: inequalities, AMC, USA(J)MO, USAMO, inequalities unsolved, 1991



Let $a = \frac{m^{m+1} + n^{n+1}}{m^m + n^n}$, where $m$ and $n$ are positive integers. Prove that $a^m + a^n \geq m^m + n^n$.