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for every n >=3 exist n different positive integers x_i with sum 1\x_i =1

Source: Norwegian Mathematical Olympiad 2021 - Abel Competition p2a

May 29, 2021
number theorySum

Problem Statement

Show that for all n≥3n\ge 3 there are nn different positive integers x1,x2,...,xnx_1,x_2, ...,x_n such that 1x1+1x2+...+1xn=1.\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}= 1.
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