高师理科学刊2026，Vol.46Issue(5)：7-11,34,6.DOI:10.3969/j.issn.1007-9831.2026.05.002
Tribonacci序列与丢番图数组
Tribonacci sequence and Diophantine tuples
龚明伟 1杨鹏1
作者信息
- 1. 辽宁科技大学 理学院,辽宁 鞍山 114051
- 折叠
摘要
Abstract
This paper studies a variant of the Diophantine tuples problem,namely,finding triples of Jacobsthal-Lucas numbers such that the product of any two plus one is a Tribonacci number.The problem can be transformed into a Diophantine equation.By using Binet formulas,the equation is rewritten in some linear forms in logarithms,an upper bound for the solutions is obtained by applying Matveev′s theorem,then a reduction method is used to reduce this bound to a computationally feasible range.Finally,with the aid of computer search,it is found that no triple satisfies the required conditions.关键词
Tribonacci序列/Jacobsthal-Lucas序列/丢番图方程/丢番图数组/对数线性型Key words
Tribonacci sequence/Jacobsthal-Lucas sequence/Diophantine equation/Diophantine tuples/linear logarithm forms分类
数理科学引用本文复制引用
龚明伟,杨鹏..Tribonacci序列与丢番图数组[J].高师理科学刊,2026,46(5):7-11,34,6.
