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MATH / What is the smallest positive integer n such that, out of the n unit fractions (1)/(k) where 1≤k≤n, exactly half of the fractions give a terminating decimal?

Problem

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problem

What is the smallest positive integer nn such that, out of the nn unit fractions 1k\frac{1}{k} where 1≤k≤n1 \le k \le n, exactly half of the fractions give a terminating decimal?
Plain-text mathematical notation (without MathML)
What is the smallest positive integer n such that, out of the n unit fractions (1)/(k) where 1≤k≤n, exactly half of the fractions give a terminating decimal?
Original LaTeX notation
What is the smallest positive integer $n$ such that, out of the $n$ unit fractions $\frac{1}{k}$ where $1 \le k \le n$, exactly half of the fractions give a terminating decimal?

level

Level 5

type

Number Theory

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Source and history

task_id
335059aa-7629-5127-bbf2-be9374cdbde6
task_key
number~5ftheory--test--335059aa-7629-5127-bbf2-be9374cdbde6
task_revision_id
1
config / split
number_theory / test

Official source

initial import