Balancing numbers which are concatenation of two repdigits

DOI10.1007/s40590-020-00293-0zbMath1455.11020OpenAlexW3026365851MaRDI QIDQ2210312

G. K. Panda, Sai Gopal Rayaguru

Publication date: 5 November 2020

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-020-00293-0

zbMATH Keywords

linear forms in logarithmsbalancing numbersrepdigits

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Radix representation; digital problems (11A63) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86) Sequences (mod (m)) (11B50)

Related Items (13)

Catalan transform of \(k\)-balancing sequences ⋮ Narayana numbers as sums of two base b repdigits ⋮ On concatenations of two Padovan and Perrin numbers ⋮ Balancing and Lucas-balancing numbers which are concatenation of three repdigits ⋮ Tribonacci numbers that are concatenations of two repdigits ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Lucas numbers which are concatenations of two repdigits ⋮ Padovan numbers which are palindromic concatenations of two distinct repdigits ⋮ Generalized Lucas numbers which are concatenations of two repdigits ⋮ Associated Pell numbers which are repdigits or concatenation of two repdigits ⋮ Tribonacci numbers with two blocks of repdigits ⋮ Padovan numbers that are concatenations of two distinct repdigits

Uses Software

• Mathematica

Cites Work

• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Repdigits as products of consecutive balancing or Lucas-balancing numbers
• Fibonacci numbers which are concatenations of two repdigits
• Repdigits in the base $b$ as sums of four balancing numbers
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