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Published online by Cambridge University Press: 28 July 2022
Solving quadratic Diophantine equations amounts to finding the values taken by quadratic forms, a problem that can be fruitfully approached by finding the equivalents of a given form under change of variables. This approach was initiated by Lagrange and developed to a high level by Gauss. However, the way Gauss did it involved an apparently difficult operation called composition of forms, clarified only later by the concept of Abelian group.
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