MathDB
Another SL problem about fibonacci numbers :3

Source: ISL 2020 C4

July 20, 2021
FibonaccicombinatoricsIMO ShortlistIMO Shortlist 2020additive representation

Problem Statement

The Fibonacci numbers F0,F1,F2,...F_0, F_1, F_2, . . . are defined inductively by F0=0,F1=1F_0=0, F_1=1, and Fn+1=Fn+Fn−1F_{n+1}=F_n+F_{n-1} for n≥1n \ge 1. Given an integer n≥2n \ge 2, determine the smallest size of a set SS of integers such that for every k=2,3,...,nk=2, 3, . . . , n there exist some x,y∈Sx, y \in S such that x−y=Fkx-y=F_k.
Proposed by Croatia
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