benchmarks.wiki / Public workspace
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Omni-MATH / We call the pair (m,n) of positive integers a happy pair if the greatest common divisor of m and n is a perfect square. For example, (20,24) is a happy pair because the greatest co…
Problem
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problem
We call the pair of positive integers a happy pair if the greatest common divisor of and is a perfect square. For example, is a happy pair because the greatest common divisor of 20 and 24 is 4. Suppose that is a positive integer such that is a happy pair. What is the number of possible values of with ?
Plain-text mathematical notation (without MathML)
We call the pair (m,n) of positive integers a happy pair if the greatest common divisor of m and n is a perfect square. For example, (20,24) is a happy pair because the greatest common divisor of 20 and 24 is 4. Suppose that k is a positive integer such that (205800,35k) is a happy pair. What is the number of possible values of k with k≤2940?
Original LaTeX notation
We call the pair $(m, n)$ of positive integers a happy pair if the greatest common divisor of $m$ and $n$ is a perfect square. For example, $(20, 24)$ is a happy pair because the greatest common divisor of 20 and 24 is 4. Suppose that $k$ is a positive integer such that $(205800, 35k)$ is a happy pair. What is the number of possible values of $k$ with $k \leq 2940$?
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Source and history
- task_id
b986a89a-28bf-583f-be7d-f92f17e6b70f- task_key
test--b986a89a-28bf-583f-be7d-f92f17e6b70f- task_revision_id
- 1
- config / split
- / test
initial import