Binary quadratic forms and the factorization method of Gauss
In Disquisitiones Arithmeticae, Gauss studied binary quadratic forms and introduced a very general version of a composition operator that allows composing even forms of different discriminants and imprimitive forms. Section V of Disquisitiones contains truly revolutionary ideas and involves very complicated computations, sometimes left to the reader. With this theory, Gauss develops a method of factorization using quadratic residues obtained by binary quadratic forms. In this work we explore Gauss method making many of the computations necessary to better understand his work.
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