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 whether a given integer is a perfect power. If it is a perfect power, return a pair
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
(9,2) are valid solutions. If a number is a perfect power, return any pair that proves it.
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