A Counting Proof for When 2 Is a Quadratic Residue

Karthik Chandrasekhar; Richard Ehrenborg; Frits Beukers

doi:10.1080/00029890.2020.1790925

A Counting Proof for When 2 Is a Quadratic Residue

Karthik Chandrasekhar, Richard Ehrenborg, Frits Beukers

Mathematics

Research output: Contribution to journal › Comment/debate

Abstract

Using the group consisting of the eight Möbius transformations x,–x, 1/x, −1/x, (x − 1)/(x + 1), (x + 1)/(1 − x), (x + 1)/(x − 1), and (1 − x)/(x + 1), we present an enumerative proof of the classical result for when the element 2 is a quadratic residue in the finite field F_q.

Original language	English
Pages (from-to)	750-751
Number of pages	2
Journal	American Mathematical Monthly
Volume	127
Issue number	8
DOIs	https://doi.org/10.1080/00029890.2020.1790925
State	Published - Sep 13 2020

Bibliographical note

Publisher Copyright:
© 2020, THE MATHEMATICAL ASSOCIATION OF AMERICA.

Funding

The authors thank David Leep for suggestions that improved the exposition of an earlier version of this note. This work was partially supported by a grant from the Simons Foundation (#429370 to Richard Ehrenborg).

Funders	Funder number
Simons Foundation	429370

Keywords

MSC: Primary 11A07

ASJC Scopus subject areas

General Mathematics

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10.1080/00029890.2020.1790925

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A Counting Proof for When 2 Is a Quadratic Residue

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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