On the sum of fourth powers in arithmetic progression-Reference-Cited by-同舟云学术

On the sum of fourth powers in arithmetic progression

Published:2020-10-29 Issue:01 Volume:17 Page:191-221
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

van Langen Joey M.¹

Affiliation:

1. Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111 1081 HV Amsterdam, The Netherlands

Abstract

We prove that the equation [Formula: see text] has no integer solutions [Formula: see text] with [Formula: see text] for all integers [Formula: see text]. We mainly use a modular approach with two Frey [Formula: see text]-curves defined over the field [Formula: see text].

Funder

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042121500093

Reference30 articles.

1. Twists of newforms and pseudo-eigenvalues ofW-operators

2. Multi-Frey ℚ-curves and the Diophantine equationa2+b6=cn

3. On the equation a3+ b3n= c2

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