MathDB
Smallest value of adjective function f(25)

Source: Bangladesh Mathematical Olympiad 2021 Problem 12

February 26, 2022
algebrafunctional equation

Problem Statement

A function g:Z→Zg: \mathbb{Z} \to \mathbb{Z} is called adjective if g(m)+g(n)>max(m2,n2)g(m)+g(n)>max(m^2,n^2) for any pair of integers mm and nn. Let ff be an adjective function such that the value of f(1)+f(2)+⋯+f(30)f(1)+f(2)+\dots+f(30) is minimized. Find the smallest possible value of f(25)f(25).
Back to ProblemsView on AoPS