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Product of Numbers and Their Floors

Source: 2012 AIME II Problem 10

March 29, 2012
floor functionAMC

Problem Statement

Find the number of positive integers nn less than 10001000 for which there exists a positive real number xx such that n=x⌊x⌋n = x \lfloor x \rfloor. Note: ⌊x⌋\lfloor x \rfloor is the greatest integer less than or equal to xx.
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