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Omni-MATH / 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. [i]

Problem

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problem

Find all positive integers nn such that there exists a sequence of positive integers a1a_1, a2a_2,…\ldots, ana_n satisfying: ak+1=ak2+1ak−1+1−1a_{k+1}=\frac{a_k^2+1}{a_{k-1}+1}-1 for every kk with 2≤k≤n−12\leq k\leq n-1. [i]
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.

[i]
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 $2\leq k\leq n-1$.

[i]

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Source and history

task_id
638246c9-7d4c-50fb-8a29-0c0d6d2a91ce
task_key
test--638246c9-7d4c-50fb-8a29-0c0d6d2a91ce
task_revision_id
1
config / split
/ test

Official source

initial import