MathNet 2022-part-02 — 197 problems (EN–VI) Question 181

Let $n$ be an integer, and let $A$ be a subset of $\{0, 1, 2, 3, \dots, 5^n\}$ consisting of $4n+2$ numbers. Prove that there exist $a, b, c \in A$ such that $a \lt b \lt c$ and $c + 2a \gt 3b$.