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Omni-MATH / While waiting for their next class on Killian Court, Alesha and Belinda both…

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problem

While waiting for their next class on Killian Court, Alesha and Belinda both write the same sequence SS on a piece of paper, where SS is a 2020-term strictly increasing geometric sequence with an integer common ratio rr. Every second, Alesha erases the two smallest terms on her paper and replaces them with their geometric mean, while Belinda erases the two largest terms in her paper and replaces them with their geometric mean. They continue this process until Alesha is left with a single value AA and Belinda is left with a single value BB. Let r0r_{0} be the minimal value of rr such that AB\frac{A}{B} is an integer. If dd is the number of positive factors of r0r_{0}, what is the closest integer to log2d\log _{2} d ?
Plain-text mathematical notation (without MathML)
While waiting for their next class on Killian Court, Alesha and Belinda both write the same sequence S on a piece of paper, where S is a 2020-term strictly increasing geometric sequence with an integer common ratio r. Every second, Alesha erases the two smallest terms on her paper and replaces them with their geometric mean, while Belinda erases the two largest terms in her paper and replaces them with their geometric mean. They continue this process until Alesha is left with a single value A and Belinda is left with a single value B. Let r₀ be the minimal value of r such that (A)/(B) is an integer. If d is the number of positive factors of r₀, what is the closest integer to log₂d ?
Original LaTeX notation
While waiting for their next class on Killian Court, Alesha and Belinda both write the same sequence $S$ on a piece of paper, where $S$ is a 2020-term strictly increasing geometric sequence with an integer common ratio $r$. Every second, Alesha erases the two smallest terms on her paper and replaces them with their geometric mean, while Belinda erases the two largest terms in her paper and replaces them with their geometric mean. They continue this process until Alesha is left with a single value $A$ and Belinda is left with a single value $B$. Let $r_{0}$ be the minimal value of $r$ such that $\frac{A}{B}$ is an integer. If $d$ is the number of positive factors of $r_{0}$, what is the closest integer to $\log _{2} d$ ?

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Source and history

task_id
415e85aa-7c23-5a0f-94c0-4656a4941b4e
task_key
test--415e85aa-7c23-5a0f-94c0-4656a4941b4e
task_revision_id
1
config / split
/ test

Official source

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