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IMO LongList 1967, Bulgaria 2

Source: IMO LongList 1967, Bulgaria 2

November 14, 2004
factorialInequalityIMO ShortlistIMO Longlist

Problem Statement

Prove that 13n2+12n+16≥(n!)2n,\frac{1}{3}n^2 + \frac{1}{2}n + \frac{1}{6} \geq (n!)^{\frac{2}{n}}, and let n≥1n \geq 1 be an integer. Prove that this inequality is only possible in the case n=1.n = 1.
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