MathNet 2022-part-05 — 197 problems (EN–VI) Question 68

Prove that for every subset $A$ of $\{1, 2, 3, ..., 5^{505}\}$ with exactly $2022$ elements, there exist three elements $a, b, c$ of $A$ with $a \lt b \lt c$ and $c + 2a \gt 3b$.