Linear Groups and Square Properties in Rings

Benjamin Fine, Fairfield University

Copyright 2016 Betty Jones and Sisters Publishing

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In [1] a proof was given of Fermat’s Two-Square Theorem using the group theoretical structure of the classical modular group. This has been extended in many directions and to other square properties in general rings. In particular in [2] a two-square theorem was given for the Gaussian integers in terms of when i is a quadratic residue. In this note we examine and survey this technique and the corresponding results and extensions.