On Ternary Diophantine Equations Of Signature (P, P, 2) Over Number Fields

Autor:	Ekin Ozman, Yasemin Kara, Erman Işik
Rok vydání:	2020
Předmět:	Combinatorics Fermat's Last Theorem Mathematics::Number Theory General Mathematics Diophantine equation Exponent Totally real number field Type (model theory) Algebraic number field Ring of integers Fermat equation generalized Fermat equation S-units modularity Prime (order theory) Mathematics
Zdroj:	Volume: 44, Issue: 4 1197-1211 Turkish Journal of Mathematics
ISSN:	1300-0098 1303-6149
Popis:	Let $K$ be a totally real number field with narrow class number one and $O_K$ be its ring of integers. We prove that there is a constant $B_K$ depending only on $K$ such that for any prime exponent $p>B_K$ the Fermat type equation $x^p+y^p=z^2$ with $x,y,z\in O_K$ does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d37a5fd6a05c176f2178dc5b27062aa2 https://aperta.ulakbim.gov.tr/record/10545 Zobrazit plný text záznamu