Tootfinder

The Generalized Fermat Equation $x^2 y^3 = z^{25}$
Nuno Freitas, Michael Stoll
https://arxiv.org/abs/2506.10667 https://arxiv.org/p…

The Generalized Fermat Equation $x^2 + y^3 = z^{25}$
We consider the generalized Fermat equation (*) $x^2 + y^3 = z^{25}$. Using the known parameterization of the primitive integral solutions to $x^2 + y^3 = z^5$ (due to Edwards), we reduce the solution of (*) to the solution of five specific equations of the form $H(u,v) = w^5$, where $H$ is homogeneous of degree $10$ with coefficients in a sextic number field $K$, $u$ and $v$ are coprime (rational) integers, and $w \in K$.

FermŠt, which uses AI to analyze e-commerce store performance and audience behavior for personalized campaigns, raised a $45M Series B led by VMG Partners (Chris Metinko/Axios)
https://www.axios.com/pro/enterprise-software-deals/2…

Exclusive: Commerce platform Fermàt raises $45M Series B
VMG Partners led the Series B.

This https://arxiv.org/abs/2402.14287 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tropical Fermat-Weber Polytropes
We study the geometry of tropical Fermat-Weber points in terms of the symmetric tropical metric over the tropical projective torus. It is well-known that a tropical Fermat-Weber point of a given sample is not unique and we show that the set of all possible Fermat-Weber points forms a polytrope. To prove this, we show that the tropical Fermat-Weber is the dual of a minimum-cost flow problem, and that its polytrope is a bounded cell of a tropical hyperplane arrangement given by both max- and min-…

Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new $\zeta$-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence
Jan Moser
https://arxiv.org/abs/2506.01706

Jacob's ladders, E. C. Titchmarsh's hypothesis (1934) and new $ζ$-equivalents of the Fermat-Wiles theorem or connections between Fermat's rationals and the Gram's sequence
In connection of our proof (1980) of the Titchmarsh's hypothesis (1934), we have obtained two asymptotic formulae (1991). In this paper we obtain three new $ζ$-equivalents of the Fermat-Wiles theorem based on the mentioned asymptotic formulae.