Balancing and Lucas-Balancing Numbers as the Difference of Two Repdigits
Balancing and Lucas-Balancing Numbers as the Difference of Two Repdigits
Positive integers with all digits equal are called repdigits. In this paper, we find all balancing and Lucas-balancing numbers, which can be expressed as the difference of two repdigits. The method of proof involves the application of Baker's theory for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure.
13 pages. arXiv admin note: text overlap with arXiv:2405.04801
Mathematics - Number Theory, Primary 11B39, Secondary 11J86, 11D61, FOS: Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Number Theory (math.NT)
Mathematics - Number Theory, Primary 11B39, Secondary 11J86, 11D61, FOS: Mathematics, Fibonacci and Lucas numbers and polynomials and generalizations, Number Theory (math.NT)
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