# Nonexistence of a Composition Law

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

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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