Largest Nth Power - Maple Help

Home : Support : Online Help : Mathematics : Number Theory : Largest Nth Power

NumberTheory

 LargestNthPower
 largest integer power divisor of a number

 Calling Sequence LargestNthPower(m, n)

Parameters

 m - integer n - positive integer

Description

 • The LargestNthPower(m, n) command computes the greatest positive integer $b$ such that ${b}^{n}$ divides m.
 • Every positive integer is a divisor of 0, so there is no greatest positive integer $b$ such that ${b}^{n}$ divides 0. For this reason, LargestNthPower(0, n) returns an error.

Examples

 > $\mathrm{with}\left(\mathrm{NumberTheory}\right):$
 > $\mathrm{LargestNthPower}\left({m}^{2},1\right)$
 ${{m}}^{{2}}$ (1)
 > $\mathrm{LargestNthPower}\left(-1,\mathrm{exp}\left(k\right)\right)$
 ${1}$ (2)
 > $\mathrm{LargestNthPower}\left(0,k\right)$

The greatest integer power divisor can be seen from the prime factorization.

 > $\mathrm{LargestNthPower}\left({2}^{2}{3}^{4}{5}^{3},2\right)$
 ${90}$ (3)
 > $\mathrm{ifactor}\left(90\right)$
 $\left({2}\right){}{\left({3}\right)}^{{2}}{}\left({5}\right)$ (4)

Compatibility

 • The NumberTheory[LargestNthPower] command was introduced in Maple 2016.