Tootfinder

Mailbag: Should Cowboys trade first-round pick? https://www.dallascowboys.com/news/mailbag-should-cowboys-trade-first-round-pick

(a,b)-Fibonacci-Legendre Cordial Graphs and k-Pisano-Legendre Primes
J. D. Andoyo
https://arxiv.org/abs/2601.10561 https://arxiv.org/pdf/2601.10561<…

Nerd sniped myself this time: after getting sniped yesterday with showing that for primes `p >= 5` that `24 | p^2 - 1`, I decided to look at primes `p, q` where `p, q >= 5` and see if `24 | p^2 - q^2`.
#math #nerdsnipe

Geometric configuration of integrally closed Noetherian domains
Gyu Whan Chang, Giulio Peruginelli
https://arxiv.org/abs/2601.22314 https://arxiv.org/pdf/2601.22314 https://arxiv.org/html/2601.22314
arXiv:2601.22314v1 Announce Type: new
Abstract: In this paper, we completely describe the family of integrally closed Noetherian domains between $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$. We accomplish this result by classifying the Krull domains between these two polynomial rings. To this end, we first describe the DVRs of $\mathbb{Q}(X)$ lying over $\mathbb{Z}_{(p)}$ for some prime $p \in \mathbb{Z}$, by distinguishing them according to whether the extension of the residue fields is algebraic or transcendental. We unify the known descriptions of such valuations by considering ultrametric balls in $\mathbb{C}_p$, the completion of the algebraic closure of the field $\mathbb{Q}_p$ of $p$-adic numbers. We then study when the intersection $R$ of such DVRs with $\mathbb{Q}[X]$ is of finite character, so that $R$ is a Krull domain, and we finally compute the divisor class group of $R$. It turns out that such a ring is formed by those polynomials which simultaneously map a finite union of ultrametric balls of $\mathbb{C}_p$ to its valuation domain $\mathbb{O}_p$, as $p\in\mathbb{Z}$ ranges through the set of primes. By a result of Heinzer, the Krull domains of this class are precisely the integrally closed Noetherian domains between $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$. This novel approach provides a geometric understanding of this class of integrally closed domains. Furthermore, we also describe the UFDs between $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$.
toXiv_bot_toot

Une tristesse vaudoise en plus. le Conseil d’Etat économise en cachette sur le dos des assurés LaMal. Qu’est-ce qui arrive Š mon canton? Quel gâchis en trois ans!
https://www.rts.ch/info/regions/vaud/2026/article/vaud-subsides-maladie-reduits-malgre-la-hausse-des-primes-d-assurance-29125234.html

Deux tiers des Suisses ont des problèmes Š payer leurs primes de caisse maladie - même avec subsides. https://www.rts.ch/audio-podcast/2026/audio/forum-29160551.html