Work

k-Diophantine m-tuples in finite fields

Year: 2022

Type: article

Abstract: In this paper, we define a [Formula: see text]-Diophantine [Formula: see text]-tuple to be a set of [Formula: see text] positive integers such that the product of any [Formula: see text] distinct positive integers is one less than a perfect square. We study these sets in finite fields [Formula: see text] for odd prime [Formula: see text] and guarantee the existence of a [Formula: see text]-Diophantine [Formula: see text]-tuple provided [Formula: see text] is larger than some explicit lower bound. We also give a formula for the number of 3-Diophantine triples in [Formula: see text] as well as an asymptotic formula for the number of [Formula: see text]-Diophantine [Formula: see text]-tuples.

Source: International Journal of Number Theory

DOI: 10.1142/s1793042123500458

Authors: Trajan Hammonds, Seoyoung Kim, Steven J. Miller, Arjun Nigam, Kyle Onghai, Dishant Saikia, Lalit M. Sharma

Institutions: Princeton University, Queen's University, Williams College, University of Arizona, University of California, Los Angeles, Tezpur University, University of Delhi

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4295093710

FWCI: 1.798

Cites: 16

Cited by: 6

Related to: 10