2021/09/08 by Sarah Marklund, Marklund, Sarah, Evangeline Tweddle +1
Mathematics · #11D41 (Secondary) #52C23 (Primary) 11D09 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2109.03440
openalex publication_date 2021/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.