2021/09/08 by Sarah Marklund, Marklund, Sarah, Evangeline Tweddle +1
Mathematics · #11D41 (Secondary) #52C23 (Primary) 11D09 #Algebra over a field #Algebraic Geometry and Number Theory #Combinatorics #Computer science #Counterexample #Diophantine equation #Discrete mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Fermat's Last Theorem #Fibonacci number #Geometry #History and Theory of Mathematics #Mathematics #Mathematics and Applications #Pure mathematics #Pythagorean theorem #Pythagorean triple #Ring (chemistry) #Set (abstract data type) #math.DS #msc:11D09 #msc:11D41 #msc:52C23
paper · pdf · doi:10.48550/arxiv.2109.03440
published in arXiv (Cornell University) (Cornell University) · 13 pages
arxiv created 2021/09/08 · openalex publication_date 2021/09/08 · arxiv updated 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
In this paper we give a description of all Pythagorean triples in the ring \mathbb Z[τ]. We also consider triples in the Fibonacci model set which satisfy the Diophantine equations arising from Fermat's Last Theorem. Examples are provided, including a counterexample to Fermat's Last Theorem for the third degree in the Fibonacci model set.