Day #29: What's a Perfect Power anyway?
- Difficulty: 5 kyu
- Solution Class: PerfectPower.java
- Test Class: PerfectPowerTest.java
- Solved: Monday, May 16th, 2016
Description:
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, 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}