A Counting Proof for When 2 Is a Quadratic Residue

Karthik Chandrasekhar; Richard Ehrenborg; F. Beukers

doi:10.1080/00029890.2020.1790925

A Counting Proof for When 2 Is a Quadratic Residue

Karthik Chandrasekhar
, Richard Ehrenborg
, F. Beukers

Research output: Contribution to journal › Article › Academic › peer-review

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 Fq .

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
Publication status	Published - 2020

Keywords

quadratic residue

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abstract = "Using the group consisting of the eight M{\"o}bius 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 Fq .",

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AU - Beukers, F.

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AB - 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 Fq .

KW - quadratic residue

U2 - 10.1080/00029890.2020.1790925

DO - 10.1080/00029890.2020.1790925

M3 - Article

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VL - 127

SP - 750

EP - 751

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 8

ER -

A Counting Proof for When 2 Is a Quadratic Residue

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