Pell and Pell-Lucas numbers which are concatenations of three repdigits

被引：0
|
作者：
Erduvan, Fatih [1 ]
Duman, Merve Guney [2 ]
机构：
[1] Izmit Namik Kemal High Sch, MEB, Kocaeli, Turkiye
[2] Sakarya Univ Appl Sci, Dept Fundamental Sci Engn, Sakarya, Turkiye
来源：
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年
关键词：
Linear forms in logarithms; Pell number; Pell-Lucas number; Repdigit; Diophantine equations; Concatenations;
D O I：
10.1007/s13226-024-00557-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, we focus on finding the Pell and Pell-Lucas numbers which are concatenations of three repdigits. We show that these numbers are 169, 408, 985 and 198, 478, 1154, respectively. We use a lemma that provides a large upper bound for the subscript n in the equations and Baker's theory of lower bounds for a nonzero linear form in logarithms of algebraic numbers. In addition, continued fraction expansions of some irrational numbers were calculated to show that some inequalities have no solution.
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页数：16
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