You are here

Quadratic Residues and the Frobenius Coin Problem

by Michael Z. Spivey (University of Puget Sound)

This article originally appeared in:
Mathematics Magazine
February, 2007

Subject classification(s): Number Theory | Algebra and Number Theory
Applicable Course(s): 4.3 Number Theory

An odd prime \(p\) has \((p-1)/2\) quadratic residues mod \(p\), and for relatively prime \(p\) and \(q\) there are \((p-1)(q-1)/2\) non-representable Frobenius numbers. The author discusses a relationship between quadratic residues and the Frobenius numbers that accounts for the presence of \((p-1)/2\) in both expressions.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Capsule Course Topic(s):
Number Theory | Congruences, Solving Congruence Equations
Number Theory | Numbers With Special Forms or Properties
Average: 3 (5 votes)

Dummy View - NOT TO BE DELETED