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Omni-MATH / Let a₁,a₂,… be an infinite sequence of integers such that a_(i) divides a_(i+1) for all i≥1, and let b_(i) be the remainder when a_(i) is divided by 210. What is the maximal number…

Problem

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problem

Let a1,a2,…a_{1}, a_{2}, \ldots be an infinite sequence of integers such that aia_{i} divides ai+1a_{i+1} for all i≥1i \geq 1, and let bib_{i} be the remainder when aia_{i} is divided by 210. What is the maximal number of distinct terms in the sequence b1,b2,…b_{1}, b_{2}, \ldots?
Plain-text mathematical notation (without MathML)
Let a₁,a₂,… be an infinite sequence of integers such that a_(i) divides a_(i+1) for all i≥1, and let b_(i) be the remainder when a_(i) is divided by 210. What is the maximal number of distinct terms in the sequence b₁,b₂,…?
Original LaTeX notation
Let \(a_{1}, a_{2}, \ldots\) be an infinite sequence of integers such that \(a_{i}\) divides \(a_{i+1}\) for all \(i \geq 1\), and let \(b_{i}\) be the remainder when \(a_{i}\) is divided by 210. What is the maximal number of distinct terms in the sequence \(b_{1}, b_{2}, \ldots\)?

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Source and history

task_id
3f30b004-ff68-530e-b959-f1a2fb0596d8
task_key
test--3f30b004-ff68-530e-b959-f1a2fb0596d8
task_revision_id
1
config / split
/ test

Official source

initial import