JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 25-30.doi: 10.6040/j.issn.1671-9352.0.2022.459

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Balancing numbers which are concatenations of three repdigits

Shanshan ZHU(),Yunyun QU*(),Jianhua ZHOU   

  1. School of Mathematical Sciences, Guizhou Normal University, Gui'an New Area 550025, Guizhou, China
  • Received:2022-09-07 Online:2023-06-20 Published:2023-05-23
  • Contact: Yunyun QU E-mail:643399108@qq.com;qucloud@163.com

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Abstract:

It is proved that 204 and 1 189 are the only Balancing numbers which are concatenations of three repdigits by using the linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction method.

Key words: Balancing number, linear form in logarithm, Baker-Davenport reduction method, repdigit

CLC Number: 

  • O156
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