IMO 2020 Shortlist C4
The Fibonacci numbers F0,F1,F2,... are defined inductively by F0 “ 0, F1 “ 1, and Fn1 “ Fn Fn´1 for n ě 1. Given an inte...
Category: Combinatorics
Problem
The Fibonacci numbers F0,F1,F2,... are defined inductively by F0 “ 0, F1 “ 1, and
Fn1 “ Fn Fn´1 for n ě 1. Given an integer n ě 2, determine the smallest size of a set S of
integers such that for every k “ 2,3,...,n there exist some x,y P S such that x ´ y “ Fk.
(Croatia)