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MATH / Let n be the smallest positive integer such that mn is a perfect kth power of an integer for some k≥2, where m=2¹⁹⁸⁰⋅3³⁸⁴⋅5¹⁶⁹⁴⋅7³⁴³. What is n+k?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let nn be the smallest positive integer such that mnmn is a perfect kkth power of an integer for some k≥2k \ge 2, where m=21980⋅3384⋅51694⋅7343m=2^{1980} \cdot 3^{384} \cdot 5^{1694} \cdot 7^{343}. What is n+kn+k?
Plain-text mathematical notation (without MathML)
Let n be the smallest positive integer such that mn is a perfect kth power of an integer for some k≥2, where m=2¹⁹⁸⁰⋅3³⁸⁴⋅5¹⁶⁹⁴⋅7³⁴³. What is n+k?
Original LaTeX notation
Let $n$ be the smallest positive integer such that $mn$ is a perfect $k$th power of an integer for some $k \ge 2$, where $m=2^{1980} \cdot 3^{384} \cdot 5^{1694} \cdot 7^{343}$. What is $n+k$?

level

Level 5

type

Number Theory

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Source and history

task_id
8bec1334-c0aa-54d1-b0e8-f43088f8c347
task_key
number~5ftheory--test--8bec1334-c0aa-54d1-b0e8-f43088f8c347
task_revision_id
1
config / split
number_theory / test

Official source

initial import