MathDB
Largest n

Source: JBMO Shortlist 2012 A5

February 4, 2015
inequalitiesinequalities proposed

Problem Statement

Find the largest positive integer nn for which the inequality a+b+cabc+1+abcn≤52 \frac{a+b+c}{abc+1}+\sqrt[n]{abc} \leq \frac{5}{2} holds true for all a,b,c∈[0,1]a, b, c \in [0,1]. Here we make the convention abc1=abc\sqrt[1]{abc}=abc.
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