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Omni-MATH / Let n≥2 be a given integer. Find the greatest value of N, for which the following is true: there are infinitely many ways to find N consecutive integers such that none of them has …

Problem

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problem

Let n≥2n\ge 2 be a given integer. Find the greatest value of NN, for which the following is true: there are infinitely many ways to find NN consecutive integers such that none of them has a divisor greater than 11 that is a perfect nthn^{\mathrm{th}} power.
Plain-text mathematical notation (without MathML)
Let n≥2 be a given integer. Find the greatest value of N, for which the following is true: there are infinitely many ways to find N consecutive integers such that none of them has a divisor greater than 1 that is a perfect n^(th) power.
Original LaTeX notation
Let $n\ge 2$ be a given integer. Find the greatest value of $N$, for which the following is true: there are infinitely many ways to find $N$ consecutive integers such that none of them has a divisor greater than $1$ that is a perfect $n^{\mathrm{th}}$ power.

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Source and history

task_id
4b835151-d62b-542f-b1e4-00b9dc622dd8
task_key
test--4b835151-d62b-542f-b1e4-00b9dc622dd8
task_revision_id
1
config / split
/ test

Official source

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