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