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OlympiadBench / 1883 / The Fibonacci numbers F₀,F₁,F₂,… are defined inductively by…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The Fibonacci numbers

F_{0}, F_{1}, F_{2}, \ldots

are defined inductively by

F_{0}=0, F_{1}=1

, and

F_{n+1}=F_{n}+F_{n-1}

for

n \geqslant 1

. Given an integer

n \geqslant 2

, determine the smallest size of a set

S

of integers such that for every

k=2,3, \ldots, n

there exist some

x, y \in S

such that

x-y=F_{k}

Plain-text mathematical notation (without MathML)

The Fibonacci numbers F₀,F₁,F₂,… are defined inductively by F₀=0,F₁=1, and F_(n+1)=F_(n)+F_(n−1) for n≥1. Given an integer n≥2, determine the smallest size of a set S of integers such that for every k=2,3,…,n there exist some x,y∈S such that x−y=F_(k).

Original LaTeX notation

The Fibonacci numbers $F_{0}, F_{1}, F_{2}, \ldots$ are defined inductively by $F_{0}=0, F_{1}=1$, and $F_{n+1}=F_{n}+F_{n-1}$ for $n \geqslant 1$. Given an integer $n \geqslant 2$, determine the smallest size of a set $S$ of integers such that for every $k=2,3, \ldots, n$ there exist some $x, y \in S$ such that $x-y=F_{k}$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1883
task_id: bb32d20f-cbf2-58af-a267-b0705589b6c3
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1883
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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