Work

On Consecutive Residues and Nonresidues Under a Linear Map in a Finite Field

Year: 2024

Type: article

Abstract: For fixed m and a, we give an explicit description of those subsets of ${\mathbb F}_{q}$ , q odd, for which both x and $mx+a$ are quadratic residues (and other combinations). These results extend and refine results that date back to Gauss.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972724000698

Authors: EMILY BERGMAN, ROBERT S. COULTER, BRADLEY FAIN

Institution: University of Delaware

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

OpenAlex ID: W4403341331

FWCI:

Cites: 9

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Related to: 10