Solution: 2021-09 Monochromatic solution of an equation

For given $$k\in \mathbb{N}$$, determine the minimum natural number $$n$$ satisfying the following: no matter how one colors each number in $$\{1,2,\dots, n\}$$ red or blue, there always exists (not necessarily distinct) numbers $$x_0, x_1,\dots, x_k \in [n]$$ with the same color satisfying $$x_1+\dots + x_k = x_0$$.

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Here is his/her solution of problem 2021-09.

Other solutions were submitted by 고성훈 (수리과학과 2018학번, +3), 김기수 (수리과학과 2018학번, +3).

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