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sum k_1=2n-3, sum 1/k_i=3

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) sl-7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 15, 2022
algebrasystem of equationsSystem

Problem Statement

Given k1,k2,...,kn∈R+k_1,k_2,...,k_n\in R^+, find all the naturals nn such that k1+k2+...+kn=2n−3k_1+k_2+...+k_n=2n-3 1k1+1k2+...+1kn=3\frac{1}{k_1}+\frac{1}{k_2}+...+\frac{1}{k_n}=3 (Zhuge Liang)
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