New posts in Algebraic Number Theory

Primes represented by $x^3-21xy^2+35y^3$.

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

Reference Request: Witt Vectors

Is the representation of any prime of the form $6n+1$ as $a^2+3b^2$ essentially unique?

Class Group of the Class Number $3$ with their elements given explicitly

Diophantine equation $x^2 + xy − 3y^2 = 17$

Proving that the Diophantine equation $(11a + 5b)^2 - 223b^2 = \pm 11$ has no solutions

Ramification in a splitting field

$K^{*n}$ has finite index in $K^*$ for an infinite extension field $K$ of $\mathbb{Q}_p$?

If $x+y^3,x^2+y^2,x^3+y$ are all integers, are $x,y$ both integers?