mpz_perfect_power_p()

[Sisyphus]

Hi,

Not sure if this is a 'factorization' question, or a 'GMP' question, or a
basic math question - but since there are probably people here with
expertise in all of those areas, I'll ask it here.

>From the docs
(http://swox.com/gmp/manual/Perfect-Power-Algorithm.html#Perfect%20Power%20A
lgorithm ):
"Detecting perfect powers is required by some factorization algorithms."

By my understanding these factorization algorithms require that the
candidate not be a *prime* power, and mpz_perfect_power_p() does not address
this issue since it does not distinguish between prime powers and composite
powers.

I'm currently coding up some of these factorization algorithms for the
joy(?) of it. Can I make use of the mpz_perfect_power_p function  without
the possibility of excluding a candidate that should not be excluded ?

Also, given that this function tells us that some candidate is a perfect
power, can we then easily determine the value of that perfect power ? I
guess not .... otherwise the function would surely return that value.

Cheers,
Rob