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Omni-MATH / A positive integer n is known as an [i]interesting[/i] number if n satisfies

Problem

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problem

A positive integer

n

is known as an [i]interesting[/i] number if

n

satisfies

{\ \{\frac{n}{10^k}} \} > \frac{n}{10^{10}}

for all

k=1,2,\ldots 9

. Find the number of interesting numbers.

Plain-text mathematical notation (without MathML)

A positive integer n is known as an [i]interesting[/i] number if n satisfies
 {(n)/(10^(k))}>(n)/(10¹⁰) 
for all k=1,2,…9.
Find the number of interesting numbers.

Original LaTeX notation

A positive integer $n$ is known as an [i]interesting[/i] number if $n$ satisfies
\[{\  \{\frac{n}{10^k}} \} > \frac{n}{10^{10}} \] 
for all $k=1,2,\ldots 9$.
Find the number of interesting numbers.

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task_id: 68e232c1-9022-5ced-8f6d-dfd16f76f0d1
task_key: test--68e232c1-9022-5ced-8f6d-dfd16f76f0d1
task_revision_id: 3
config / split: / test

Official source

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