MathDB

Minimal number with certain property

Source: 43rd International Tournament of Towns, Senior A-Level P4, Fall 2021

February 18, 2023

algebraTournament of Towns

Problem Statement

What is the minimum

k{}

for which among any three nonzero real numbers there are two numbers

a{}

and

b{}

such that either

|a-b|\leqslant k

|1/a-1/b|\leqslant k

?
Maxim Didin