SOLUTIONS OF THE CUBIC FERMAT EQUATION IN QUADRATIC FIELDS

2012/11/15 by Marvin Jones, MARVIN JONES, Jeremy Rouse +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Binary quadratic form #Fermat number #Fermat's Last Theorem #Fermat's theorem on sums of two squares #Integer (computer science) #Limits and Structures in Graph Theory #Quadratic equation #Quadratic field #Square-free integer #math.NT #msc:11D41 #msc:11F37 #msc:11G05 #msc:11G40

paper · pdf · doi:10.1142/s1793042113500449

published as Int. J. Number Theory 9 (2013) , no. 6, 1579-1591 · 12 pages

arxiv created 2012/11/15 · openalex publication_date 2013/04/16 · openalex created_date 2016/06/24 · arxiv updated 2018/01/22 · openalex updated_date 2026/08/05

Abstract

We give necessary and sufficient conditions on a squarefree integer d for there to be non-trivial solutions to x 3 + y 3 = z 3 in [Formula: see text], conditional on the Birch and Swinnerton-Dyer conjecture. These conditions are similar to those obtained by J. Tunnell in his solution to the congruent number problem.

Citations

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