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Nonexistence of a Composition Law

by Şaban Alaca (Carleton University Canada) and Kenneth S. Williams (Carleton University Canada)

This article originally appeared in:
Mathematics Magazine
April, 2007

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

It is known that every positive odd integer can be expressed in the form \(x^2 + y^2 + 2z^2\) for some integers \(x\), \(y\) and \(z\). The authors discuss the non-existence of certain composition laws.

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Capsule Course Topic(s):
Number Theory | Diophantine Problems
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