6.

Part of 2014 Poland - Second Round

Problems(1)

99% fine numbers

Source: Poland 2014 - Second Round P6

Call a positive number

n

fine, if there exists a prime number

p

p|n

p^2\nmid n

. Prove that at least 99% of numbers

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

are fine numbers.

number theoryprime numbers