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MATH / Find the smallest positive integer n such that there exists r∈(0,(1)/(1000)) such that the number (n+r)³ is an integer.

Problem

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problem

Find the smallest positive integer nn such that there exists r∈(0,11000)r \in (0, \tfrac{1}{1000}) such that the number (n+r)3(n+r)^3 is an integer.
Plain-text mathematical notation (without MathML)
Find the smallest positive integer n such that there exists r∈(0,(1)/(1000)) such that the number (n+r)³ is an integer.
Original LaTeX notation
Find the smallest positive integer $n$ such that there exists $r \in (0, \tfrac{1}{1000})$ such that the number $(n+r)^3$ is an integer.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
de072a16-2331-570d-83df-11726d391db6
task_key
intermediate~5falgebra--test--de072a16-2331-570d-83df-11726d391db6
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import