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Problem 12

Part of 2021 Bangladesh Mathematical Olympiad

Problems(1)

Smallest value of adjective function f(25)

Source: Bangladesh Mathematical Olympiad 2021 Problem 12

2/26/2022
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).
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