Can I efficiently verify if given $h$ is the class number of a quadratic field?
Can I efficiently verify if given $h$ is the class number of a quadratic field?
I tried pari's Qfb and did some experiments with Lidia, but I must be missing something.
What I tried is for random $a$ compute $a^h$ but I don't get the identity and in Lidia I can't check if it is principal.