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3^{n^2} > (n!)^4

Source: Austrian Federal Competition For Advanced Students 2009, Part 1, p1

August 30, 2019
factorialexponentialExponential inequalityinequalitiesalgebradiophantineinduction

Problem Statement

Show that for all positive integer nn the following inequality holds 3n2>(n!)43^{n^2} > (n!)^4 .
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