GNU MP 6.1.0: Perfect Power Algorithm
Description: How to install and use the GNU multiple precision arithmetic library, version 6.1.0.

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#### 15.5.4 Perfect Power

Detecting perfect powers is required by some factorization algorithms. Currently `mpz_perfect_power_p` is implemented using repeated Nth root extractions, though naturally only prime roots need to be considered. (See Nth Root Algorithm.)

If a prime divisor p with multiplicity e can be found, then only roots which are divisors of e need to be considered, much reducing the work necessary. To this end divisibility by a set of small primes is checked.