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MATH / For how many positive integers m, 1≤m≤1000, does there exist at least one positive integer n such that m⋅n≤m+n?

Problem

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problem

For how many positive integers m,m, 1≤m≤1000,1 \le m \le 1000, does there exist at least one positive integer nn such that m⋅n≤m+nm \cdot n \le m + n?
Plain-text mathematical notation (without MathML)
For how many positive integers m, 1≤m≤1000, does there exist at least one positive integer n such that m⋅n≤m+n?
Original LaTeX notation
For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?

level

Level 2

type

Intermediate Algebra

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Source and history

task_id
0287e16a-fef3-5826-831f-c95209b868b5
task_key
intermediate~5falgebra--test--0287e16a-fef3-5826-831f-c95209b868b5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import