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Omni-MATH / For any integer n≥2, we define A_(n) to be the number of positive integers m with the following property: the distance from n to the nearest multiple of m is equal to the distance …

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problem

For any integer n≥2n \ge2, we define An A_n to be the number of positive integers m m with the following property: the distance from nn to the nearest multiple of mm is equal to the distance from n3n^3 to the nearest multiple of m m. Find all integers n≥2n \ge 2 for which An A_n is odd. (Note: The distance between two integers a a and bb is defined as |a−b||a -b|.)
Plain-text mathematical notation (without MathML)
For any integer n≥2, we define A_(n) to be the number of positive integers m with the following property: the distance from n to the nearest multiple of m is equal to the distance from n³ to the nearest multiple of m. Find all integers n≥2 for which A_(n) is odd. (Note: The distance between two integers a and b is defined as |a−b|.)
Original LaTeX notation
For any integer $n \ge2$, we define $ A_n$ to be the number of positive integers $ m$ with the following property: the distance from $n$ to the nearest multiple of $m$ is equal to the distance from $n^3$ to the nearest multiple of $ m$. Find all integers $n \ge 2 $ for which $ A_n$ is odd. (Note: The distance between two integers $ a$ and $b$ is defined as $|a -b|$.)

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Source and history

task_id
7299591b-18dd-5f85-a4e1-88eb43ac322c
task_key
test--7299591b-18dd-5f85-a4e1-88eb43ac322c
task_revision_id
1
config / split
/ test

Official source

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