On differences of perfect powers and prime powers

dc.contributor.author	Cazorla García, Pedro-José	es-ES
dc.date.accessioned	2025-11-12T15:03:51Z
dc.date.available	2025-11-12T15:03:51Z
dc.identifier.uri	http://hdl.handle.net/11531/107144
dc.description.abstract	.	es-ES
dc.description.abstract	Given a prime number q and a squarefree integer C1, we develop a method to explicitly determine the tuples (y, n, α) for which the difference yn − qα has squarefree part equal to C1. Our techniques include the combination of the local information provided by Galois representations of Frey–Hellegouarch curves with the effective resolution of Thue–Mahler equations, as well as the use of improved lower bounds for q−adic and complex logarithms. As an application of this methodology, we will completely resolve the case when 1 ≤ C1 ≤ 20 and 2 ≤ q < 25.	en-GB
dc.format.mimetype	application/pdf	es_ES
dc.language.iso	en-GB	es_ES
dc.rights	Creative Commons Reconocimiento-NoComercial-SinObraDerivada España	es_ES
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	es_ES
dc.title	On differences of perfect powers and prime powers	es_ES
dc.type	info:eu-repo/semantics/workingPaper	es_ES
dc.description.version	info:eu-repo/semantics/draft	es_ES
dc.rights.holder		es_ES
dc.rights.accessRights	info:eu-repo/semantics/openAccess	es_ES
dc.keywords	.	es-ES
dc.keywords	Perfect powers, prime powers, Diophantine equations, Thue–Mahler equations, Frey–Hellegouarch curves, modular method, Galois representations, Baker theory, logarithmic forms, number theory	en-GB

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