MathDB

set with c+2a>3b

Source: ISL 2021 A1

July 12, 2022

algebraIMO Shortlist2021A1ISL 2021

Problem Statement

Let

n

be a positive integer. Given is a subset

A

\{0,1,...,5^n\}

with

4n+2

elements. Prove that there exist three elements

a<b<c

from

A

such that

c+2a>3b

.
Proposed by Dominik Burek and Tomasz Ciesla, Poland