# 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): Algebra and Number Theory | 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.

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