丢番图三元{2,b, c}的可拓性

Pub Date : 2021-06-01 DOI:10.2478/auom-2021-0016

Nikola Adžaga, A. Filipin, Ana Jurasic

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引用次数: 0

摘要

摘要考虑了2 < b < c的Diophantine三元组{2,b, c}的可拓性，并证明了该集合不能被扩展到不规则的Diophantine四重组。我们成功地证明了c的一些族(取决于b)。作为推论，例如，我们证明了对于b/2−1素数，所有2 < b < c < d的Diophantine四元组{2,b, c, d}都是正则的。

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The extensibility of the Diophantine triple {2, b, c}

Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.

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