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Bernoulli's inequality

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October 11, 2005
inequalitiesAMCUSA(J)MOUSAMOinequalities unsolved1991

Problem Statement

Let a=mm+1+nn+1mm+nna = \frac{m^{m+1} + n^{n+1}}{m^m + n^n}, where mm and nn are positive integers. Prove that am+an≥mm+nna^m + a^n \geq m^m + n^n.
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