Vieta jumping and small norms in quadratic number fields
Franz Lemmermeyer
TL;DR
This paper explores the link between a well-known IMO problem and the properties of elements with small norms in quadratic number fields, focusing on parametrized units.
Contribution
It establishes a novel connection between a classic mathematical problem and the structure of quadratic number fields with small norm elements.
Findings
Identifies the relationship between the IMO problem and quadratic number fields.
Characterizes elements of small norms in quadratic fields.
Provides insights into parametrized units in these fields.
Abstract
In this article we explain the connection between the famous problemfrom the IMO 1988 and elements of small norms in quadratic number fields with parametrized units.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Meromorphic and Entire Functions