Fibonacci Numbers with a Prescribed Block of Digits

被引：20
|
作者：
Trojovsky, Pavel [1 ]
机构：
[1] Univ Hradec Kralove, Fac Sci, Dept Math, Hradec Kralove 50003, Czech Republic
来源：
MATHEMATICS | 2020年 / 8卷 / 04期
关键词：
Fibonacci numbers; digits; linear forms in logarithms; Baker-Davenport; LUCAS-NUMBERS; REPDIGITS; POWERS; SUMS;
D O I：
10.3390/math8040639
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that F22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form ab...bc... c. The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from Diophantine approximation.
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页数：7
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