Satyabrate Sahoo

collaborators

8 papers

math.NT2026

Generalized Fermat equation over cyclotomic $Z_{l}$ -extensions of totally real fields

Satyabrat Sahoo

Let $K$ be a totally real number field of odd degree in which $2$ is inert. Let $l \geq 5$ be a prime with $l ∤ [K : Q]$ and $g cd (\frac{l - 1}{2}, [K : Q]) = 1$ . We…

math.NT2026

Generalized Fruit Diophantine equation over number fields

Satyabrat Sahoo, Shanta Laishram

Let $K$ be a number field and $O_{K}$ be the ring of integers of $K$ . In this article, we study the solutions of the generalized fruit Diophantine equation $ax^d-y^2-z^2 +x…

math.NT2026

On the solutions of the generalized Fermat equation over totally real number fields

Satyabrat Sahoo

Let $K$ be a totally real number field and $O_{K}$ be the ring of integers of $K$ . In this article, we study the asymptotic solutions of the generalized Fermat equation $Ax…

math.NT2025

A survey on the generalized Fermat equation of various signatures over totally real fields

Satyabrat Sahoo

Following the famous proof of Fermat's Last Theorem by Andrew Wiles using the modularity of elliptic curves over $Q$ , significant developments have been made in the study…

math.NT2025

Effective Generalized Fermat equation of signature $(2 p, 2 q, r)$ with odd narrow class number

Satyabrat Sahoo

Fix a rational prime $r \geq 5$ . In this article, we study the integer solutions of the generalized Fermat equation of signature $(2 p, 2 q, r)$ , namely $x^{2 p} + y^{2 q} = z^{r}$ , where the…

math.NT2025

Asymptotic Fermat equation of signature $(r, r, p)$ over totally real fields

Somnath Jha, Satyabrat Sahoo

Let $K$ be a totally real number field and $O_{K}$ be the ring of integers of $K$ . This manuscript examines the asymptotic solutions of the Fermat equation of signature $(…

Generalized Fermat equation over cyclotomic Zl​-extensions of totally real fields

Generalized Fruit Diophantine equation over number fields

On the solutions of the generalized Fermat equation over totally real number fields

A survey on the generalized Fermat equation of various signatures over totally real fields

Effective Generalized Fermat equation of signature (2p,2q,r) with odd narrow class number

Asymptotic Fermat equation of signature (r,r,p) over totally real fields

Generalized Fermat equation over cyclotomic $Z_{l}$ -extensions of totally real fields

Effective Generalized Fermat equation of signature $(2 p, 2 q, r)$ with odd narrow class number

Asymptotic Fermat equation of signature $(r, r, p)$ over totally real fields