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Benelux Olympiad 2020, Problem 4 (close divisors of integers)

Source: BxMO 2020, Problem 4

May 2, 2020
number theoryBxMOBenelux

Problem Statement

A divisor dd of a positive integer nn is said to be a close divisor of nn if n<d<2n\sqrt{n}<d<2\sqrt{n}. Does there exist a positive integer with exactly 20202020 close divisors?
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