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#40 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 mk = n.

Your task is to check wheter a given integer is a perfect power. If it is a perfect power, return a pair m and k with mk = 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}

public class PerfectPower {
    public static int[] isPerfectPower(int n) {
        for (int i = 2; i < Math.log(n) / Math.log(2) + 1; i++) {
            for (int j = 2; Math.pow(j, i) <= n; j++) {
                if (Math.pow(j, i) == n) {
                    return new int[]{j, i};
                }
            }
        }
        return null;
    }
}