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OlympiadBench / 2111 / Find all positive integers n such that there exists a sequence of positive…

Problem

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

question

Find all positive integers

n

such that there exists a sequence of positive integers

a_{1}, a_{2}, \ldots, a_{n}

satisfying

a_{k+1}=\frac{a_{k}^{2}+1}{a_{k-1}+1}-1

for every

k

with

2 \leq k \leq n-1

Plain-text mathematical notation (without MathML)

Find all positive integers n such that there exists a sequence of positive integers a₁,a₂,…,a_(n) satisfying

a_(k+1)=(a_(k)²+1)/(a_(k−1)+1)−1

for every k with 2≤k≤n−1.

Original LaTeX notation

Find all positive integers $n$ such that there exists a sequence of positive integers $a_{1}, a_{2}, \ldots, a_{n}$ satisfying

$$
a_{k+1}=\frac{a_{k}^{2}+1}{a_{k-1}+1}-1
$$

for every $k$ with $2 \leq k \leq n-1$.

answer type

Numerical

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2111
task_id: 973ee150-027d-579b-9ef0-abbfefd06ff2
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2111
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import