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Joachim König's user avatar
Joachim König's user avatar
Joachim König's user avatar
Joachim König
  • Member for 5 years, 10 months
  • Last seen this week
12 votes
Accepted

If $\mathbb{C}(u(x,y),v(x,y),f(x))=\mathbb{C}(x,y)$, for every $f(x) \in \mathbb{C}[x]-\mathbb{C}$, then already $\mathbb{C}(u,v)=\mathbb{C}(x,y)$?

12 votes

Six consecutive positive integers with certain shape

11 votes
Accepted

Integer solutions of an algebraic equation

10 votes

Does there exist a number field, unramified over a predetermined finite set of primes of Q, such that the inverse regular Galois problem is correct for that number field?

10 votes

Results from abstract algebra which look wrong (but are true)

9 votes
Accepted

Covering all but finitely many integers via some given polynomials

9 votes
Accepted

Galois groups of specific classes of polynomials with one coefficient fixed

9 votes

A cyclic Galois extension over $ \mathbb{Q}(\omega)$

9 votes
Accepted

Inequality of three prime factors of $x^2-1$

8 votes

What are examples of problems we know how to solve for primes (or prime powers), but not for composites?

7 votes

Irreducibility measure of integer polynomials

7 votes
Accepted

$\mathbb{C}(u(x,y),v(x,y),f(x)+g(y))=\mathbb{C}(x,y)$ implies $\mathbb{C}(u(x,y),v(x,y))=\mathbb{C}(x,y)$?

6 votes
Accepted

Closed-form for the number of partitions of $n$ avoiding the partition $(4,3,1)$

6 votes
Accepted

Families of finite groups of which every finite group is a quotient

5 votes
Accepted

A method to generate solvable equations of degrees $p = 7, 13, 19, 31, 37,\dots$ using only cubics

5 votes
Accepted

On the refined minimal ramification problem for $p$-groups

5 votes

Number of conjugacy classes of a semi-direct product of two finite groups

5 votes

Splitting fields of degree 4 irreducible polynomials containing a fixed quadratic extension

4 votes
Accepted

Irreducible integral polynomials having roots module primes in arithmetic progressions

4 votes

Radicands of square roots of the 2020s, written in simplest radical form

4 votes
Accepted

Finding a sextic analogue to the solvable octic $\frac{(x + 1)^6(x^2 + x + 7)}x = -k^3$ where $e^{(\pi/3)\sqrt{d}}\approx k^3+41.999999999999\dots$

4 votes

On integral points of $f(x,y)=z g(x,y)$

3 votes

Dihedral extension unramified at primes dividing order of group?

3 votes
Accepted

The distribution of certain Galois groups

2 votes
Accepted

Solving solvable septics using only cubics?

2 votes

Density of extended Mersenne numbers?

2 votes
Accepted

Existence of intermediate field extensions for tamely ramified p-adic extensions

2 votes
Accepted

Unramified composition for every extension

2 votes
Accepted

Not containing $ 2^{i}$-th primitive roots of unity in cyclic galois extension of number field

1 vote
Accepted

On Elkies' $\text{9T32}$ nonic and a shared property with j-function formulas