Given $k_1,k_2,...,k_n\in R^+$, find all the naturals $n$ such that $$k_1+k_2+...+k_n=2n-3$$$$\frac{1}{k_1}+\frac{1}{k_2}+...+\frac{1}{k_n}=3$$(Zhuge Liang)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) sl-7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: algebra, system of equations, System