H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of integers and rings of polynomials over fields of odd characteristic. Also, we present new deterministic algorithms for finding the corresponding proper representations.
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机译：H. J. S. Smith使用回文连续体的概念证明了Fermat的二平方定理。在本文中，我们将Smith的方法扩展到一些可交换的欧几里得环中的适当二元二次形式表示，包括整数环和多项式环在奇特征域上。同样，我们提出了新的确定性算法，用于查找相应的适当表示形式。
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