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Maximum of products of segments determined by n points

Source: Romania TST 6 2009, Problem 3

May 5, 2012
functioncomplex analysistrigonometryinequalitiesfloor functioncomplex numbersalgebra proposed

Problem Statement

Given an integer n≥2n\geq 2 and a closed unit disc, evaluate the maximum of the product of the lengths of all n(n−1)2\frac{n(n-1)}{2} segments determined by nn points in that disc.
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