NumberTheory - Maple Programming Help

Home : Support : Online Help : Mathematics : Numbers : NumberTheory/LargestNthPower

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

 > with(NumberTheory):
 > LargestNthPower(m^2, 1);
 ${{m}}^{{2}}$ (1)
 > LargestNthPower(-1, exp(k));
 ${1}$ (2)
 > LargestNthPower(0, k);

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

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

Compatibility

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