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On the parametrization of solutions of quadratic equations. (Sur la paramétrisation des solutions des équations quadratiques.) (French) Zbl 1116.11024
Let $$Q(X,Y)$$ be a binary integral quadratic form, then if $$Q=1$$ has a solution it easily leads to an integral parametrization by quadratic forms $$q_i(s,t)$$, $$(i=1,2,3)$$ such that $$Q(q_1(s,t),q_2(s,t))=q^2_3 (s,t)$$. This also serves to make the class of $$Q$$ the square of the class of $$q_3(s,t)$$. As a consequence $$q_3$$ is independent of the solution, and there are also applications to the 2-descent for elliptic curves [see the author, LMS J. Comput. Math. 5, 7–17 (2002; Zbl 1067.11015)]. The exposition also discusses the 2-class number and is remarkably self-contained.

##### MSC:
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