I'm new user here! I'm stuck on the following and I was wondering if some NT experts can prove some help.
Question (from an entrance exam in my country) 5) What is the density of the rational primes $p$ that factor as $(p)=p_{1}p_{2}$ in $\mathbb{Q}[\sqrt[3]{2}]$. What about $\mathbb{Q}[\sqrt[5]{2}]$?
I think Chebotarev is the answer but I kno only how to use it to get the density of the primes that split completely in those number fields.