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Maximum of x_1+...+x_n subject to x_1+...+x_n=x_1...x_n

Source: Romania TST 4 2009, Problem 1

May 4, 2012
algebra proposedalgebra

Problem Statement

Given an integer n≥2n\geq 2, determine the maximum value the sum x1+⋯+xnx_1+\cdots+x_n may achieve, as the xix_i run through the positive integers, subject to x1≤x2≤⋯≤xnx_1\leq x_2\leq \cdots \leq x_n and x1+⋯+xn=x1x2⋯xnx_1+\cdots+x_n=x_1 x_2\cdots x_n.
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