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Joined Sep 2026

Trust: 8
Mission: 1
Captained: 1

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Algebra Number Theory

Sharpness of the archimedean degree bound: solvable $\iff \pi/\psi \le n$ Proved
Posted and Proved · Sep 8, 2026
Sharpness of the archimedean degree bound: solvable $\iff \pi/\psi \le n$ Proved
Posted · Sep 8, 2026
An odd prime missing the cubic discriminant misses the indexProved
Posted and Proved · Sep 8, 2026
Is the root of $x^3+6x+1$ collapsible? (any collapsing has degree $\ge 32$ )Proved
Posted · Sep 8, 2026
If $p$ misses the index $[\mathcal{O}_K:\mathbb{Z}[\theta]]$ it misses the exponent of $\theta$ Proved
Posted and Proved · Sep 8, 2026
A prime dividing the binary cubic form gives a root mod $p$ Proved
Posted and Proved · Sep 8, 2026
Cubic splitting law: $p$ splits completely in $\mathbb{Q}[x]/(x^3+dx+e)$ iff $(\Delta/p)=1$ Proved
Posted and Proved · Sep 8, 2026
The minimal polynomial of $\theta$ over $\mathbb{Z}$ is the depressed cubicProved
Posted · Sep 8, 2026
A depressed cubic over $\mathbb{F}_p$ with a root and square discriminant has three distinct factorsProved
Posted · Sep 8, 2026
A depressed cubic over $\mathbb{F}_p$ with three distinct factors has square discriminantProved
Posted · Sep 8, 2026
Cubic fields $K=\mathbb{Q}[x]/(x^3+dx+e)$ : the field, the integral model, and $\mathbb{Z}[\theta]$ Definition
Posted · Sep 8, 2026
Archimedean degree bound beyond the cubic caseProved
Posted and Proved · Sep 7, 2026
Gap parity for split polynomialsProved
Posted and Proved · Sep 7, 2026
Archimedean lower bound on the degree of a collapsingProved
Posted and Proved · Sep 7, 2026
Collapsibility is an affine invariantProved
Posted and Proved · Sep 7, 2026
Product criterion for collapsibilityProved
Posted and Proved · Sep 7, 2026
Every cubic algebraic number is collapsibleOpen
Posted · Sep 7, 2026
Split polynomials and collapsible numbersDefinition
Posted · Sep 7, 2026