Diophantine representations of linear recurrences. I

被引：0

作者：

Vsemirnov M.A.

机构：

来源：

Journal of Mathematical Sciences | 1998年 / 89卷 / 2期

关键词：

Additional Restriction; Algebraic Integer; Linear Recurrence; Direct Construction; Recurrent Sequence;

D O I：

10.1007/BF02355857

中图分类号：

学科分类号：

摘要：

Direct constructions of Diophantine representations of linear recurrent sequences are discussed. These constructions generalize already known results for second-order recurrences. Some connections of this problem with the theory of units in rings of algebraic integers are shown. It is proved that the required representations exist only for second-, third-, and fourth-order sequences. In the two last-mentioned cases certain additional restrictions on their coefficients must be imposed. ©1998 Plenum Publishing Corporation.

引用

页码：1113 / 1118

页数：5

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