Tribonacci numbers that are concatenations of two repdigits.

IF 1.8 2区数学 Q1 MATHEMATICS Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas Pub Date : 2020-01-01 Epub Date: 2020-09-15 DOI:10.1007/s13398-020-00933-0

Mahadi Ddamulira

{"title":"Tribonacci numbers that are concatenations of two repdigits.","authors":"Mahadi Ddamulira","doi":"10.1007/s13398-020-00933-0","DOIUrl":null,"url":null,"abstract":"<p><p>Let <math> <msub><mrow><mo>(</mo> <msub><mi>T</mi> <mi>n</mi></msub> <mo>)</mo></mrow> <mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </msub> </math> be the sequence of Tribonacci numbers defined by <math> <mrow><msub><mi>T</mi> <mn>0</mn></msub> <mo>=</mo> <mn>0</mn></mrow> </math> , <math> <mrow><msub><mi>T</mi> <mn>1</mn></msub> <mo>=</mo> <msub><mi>T</mi> <mn>2</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> , and <math> <mrow><msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>3</mn></mrow> </msub> <mo>=</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>2</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>1</mn></mrow> </msub> <mo>+</mo> <msub><mi>T</mi> <mi>n</mi></msub> </mrow> </math> for all <math><mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn></mrow> </math> . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.</p>","PeriodicalId":54471,"journal":{"name":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","volume":"114 4","pages":"203"},"PeriodicalIF":1.8000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s13398-020-00933-0","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13398-020-00933-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/9/15 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 22

Abstract

Let ${(T_{n})}_{n \geq 0}$ be the sequence of Tribonacci numbers defined by $T_{0} = 0$ , $T_{1} = T_{2} = 1$ , and $T_{n + 3} = T_{n + 2} + T_{n + 1} + T_{n}$ for all $n \geq 0$ . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

由两个拟人数字连接而成的三波那契数。

让T (n) n≥0被T Tribonacci之序列数字:0 = 0,T = T = 2 = 1, T和T n + 3 = n + 2 + T T n + 1 + n的所有n≥0。在这篇文章中，我们用下舱的线条来线性使用对数的数字和面包师减少的程序来寻找所有的数字，这些数字是两个重复的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas 数学-数学

CiteScore

4.70

自引率

17.20%

发文量

151

审稿时长

>12 weeks

期刊介绍： The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.

期刊最新文献

Supercongruences involving Domb numbers and binary quadratic forms. Absolutely closed semigroups. Homogeneous isosceles-free spaces. Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial. Richards's curve induced Banach space valued ordinary and fractional neural network approximation.