whats-a-perfect-power-anyway

What's a Perfect Power anyway?

A perfect power is a classification of positive integers:

In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that m ^k = n.

Your task is to check whether a given integer is a perfect power. If it is a perfect power, return a pair m and k with m^k = n as a proof. Otherwise return Nothing, Nil, null, NULL, None or your language's equivalent.

Note: For a perfect power, there might be several pairs. For example 81 = 3^4 = 9^2, so (3,4) and (9,2) are valid solutions. However, the tests take care of this, so if a number is a perfect power, return any pair that proves it.

Examples

isPerfectPower(4) => new int[]{2,2}
isPerfectPower(5) => null
isPerfectPower(8) => new int[]{2,3}
isPerfectPower(9) => new int[]{3,2}