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Maximizing sum of cubes

Source: Poland Math Olympiad 1992 First Round #8

June 2, 2023
algebrafactorizationsum of cubes

Problem Statement

Given is a positive integer n≥2n \geq 2. Determine the maximum value of the sum of natural numbers k1,k2,...,knk_1,k_2,...,k_n satisfying the condition: k13+k23+⋯+kn3≤7nk_1^3+k_2^3+ \dots +k_n^3 \leq 7n.
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