Perfect Power Algorithm (GNU MP 6.3.0)
Description: How to install and use the GNU multiple precision arithmetic library, version 6.3.0.

#### 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.)

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.