Points on x4 + y4 + z4 = 0 over algebraic extensions of ℚ(i)-Reference-Cited by-同舟云学术

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Points on x4 + y4 + z4 = 0 over algebraic extensions of ℚ(i)

Published:2022-10-15 Issue:04 Volume:19 Page:829-842
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Tho Nguyen Xuan¹^ORCID

Affiliation:

1. Hanoi University of Science and Technology, Hanoi, Vietnam

Abstract

It is shown that the twisted Fermat quartic [Formula: see text] has no points over any odd degree extensions of [Formula: see text]. All points over quadratic extensions of [Formula: see text] are found.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042123500410

Reference9 articles.

1. The Diophantine equation $x^4 + y^4 = 1$ in algebraic number fields

2. Pure and Applied Mathematics;Mordell L. J.,1969

3. The Fermat cubic and quartic curves over cyclic fields

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