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...

IMO 2020 Shortlist C4

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)