2004/12/15 by Alfred J. van der Poorten, van der Poorten, Alfred J., Christine S. Swart +2
Mathematics · #11B83 #11G05 (primary) 11A55 #14H05 #14H52 (secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT #msc:11A55 #msc:11B83 #msc:11G05 #msc:14H05 #msc:14H52
paper · pdf · doi:10.48550/arxiv.math/0412293
7 pages
arxiv created 2004/12/15 · openalex publication_date 2004/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In his `Memoir on Elliptic Divisibility Sequences', Morgan Ward's definition of the said sequences has the remarkable feature that it does not become at all clear until deep into the paper that there exist nontrivial such sequences. Even then, Ward's proof of coherence of his definition relies on displaying a sequence of values of quotients of Weierstraßσ-functions. We give a direct proof of coherence and show, rather more generally, that a sequence defined by a so-called Somos relation of gap 4 always also is given by a three term Somos relation of all larger gaps 5, 6, 7, ... .