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99% fine numbers

Source: Poland 2014 - Second Round P6

July 28, 2019

number theoryprime numbers

Problem Statement

Call a positive number

n

fine, if there exists a prime number

p

such that

p|n

and

p^2\nmid n

. Prove that at least 99% of numbers

1, 2, 3, \ldots, 10^{12}

are fine numbers.

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