# Quadratic Residues and the Frobenius Coin Problem

by Michael Z. Spivey (University of Puget Sound)

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.

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