International Mathematics Competition
for University Students
2024

IMC2024: Day 2, Problem 6

Problem 6. Prove that for any function \(\displaystyle f\colon\mathbb Q\to\mathbb Z \), there exist \(\displaystyle a,b,c\in\mathbb Q\) such that \(\displaystyle a < b < c \), \(\displaystyle f(b) \geq f(a) \), and \(\displaystyle f(b) \geq f(c) \).

Mehdi Golafshan & Markus A. Whiteland, University of Liège

  Solution