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2002 AMC 10AProblem 4P1-10~1 minPrint
Diophantine EquationsAlgebraic ManipulationTest small/specific values or special cases to find or verify the answer

For how many positive integers mm does there exist at least one positive integer n such that m⋅n≤m+nm \cdot n \le m + n ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2002 12A #6.