Let K be a cubic number field of discriminant , and write where is a fundamental discriminant (including 1). Then: if and only if p is totally ramified, i.e if and only if . implies p=3. implies p=3.
See [7] for a proof.
, and write 
where 
is a fundamental discriminant
(including 1). Then:
if and only if p is totally ramified, i.e if and
only if 
.
implies p=3.
implies p=3.