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Inequality true for positive reals

Source: ITAMO 2006 Q5

May 8, 2006
inequalitiesalgebra proposedalgebra

Problem Statement

Consider the inequality (a1+a2+⋯+an)2≥4(a1a2+a2a3+⋯+ana1).(a_1+a_2+\dots+a_n)^2\ge 4(a_1a_2+a_2a_3+\cdots+a_na_1). a) Find all n≥3n\ge 3 such that the inequality is true for positive reals. b) Find all n≥3n\ge 3 such that the inequality is true for reals.
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