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Omni-MATH / We call a positive integer t good if there is a sequence a₀,a₁,… of positive integers satisfying a₀=15,a₁=t, and a_(n−1)a_(n+1)=(a_(n)−1)(a_(n)+1) for all positive integers n. Find…

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problem

We call a positive integer tt good if there is a sequence a0,a1,…a_{0}, a_{1}, \ldots of positive integers satisfying a0=15,a1=ta_{0}=15, a_{1}=t, and an−1an+1=(an−1)(an+1)a_{n-1} a_{n+1}=\left(a_{n}-1\right)\left(a_{n}+1\right) for all positive integers nn. Find the sum of all good numbers.
Plain-text mathematical notation (without MathML)
We call a positive integer t good if there is a sequence a₀,a₁,… of positive integers satisfying a₀=15,a₁=t, and a_(n−1)a_(n+1)=(a_(n)−1)(a_(n)+1) for all positive integers n. Find the sum of all good numbers.
Original LaTeX notation
We call a positive integer $t$ good if there is a sequence $a_{0}, a_{1}, \ldots$ of positive integers satisfying $a_{0}=15, a_{1}=t$, and $a_{n-1} a_{n+1}=\left(a_{n}-1\right)\left(a_{n}+1\right)$ for all positive integers $n$. Find the sum of all good numbers.

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Source and history

task_id
261c3d31-e7d6-5300-b6b7-c81f7336a52f
task_key
test--261c3d31-e7d6-5300-b6b7-c81f7336a52f
task_revision_id
1
config / split
/ test

Official source

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