Balancing and Lucas-balancing numbers as difference of two repdigits
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912259127640064 |
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| author | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| author_facet | Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Balancing and Lucas-balancing numbers as difference of two repdigits Mohapatra, Monalisa Bhoi, Pritam Kumar Panda, Gopal Krishna Number Theory Primary 11B39, Secondary 11J86, 11D61 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. |
| title | Balancing and Lucas-balancing numbers as difference of two repdigits |
| topic | Number Theory Primary 11B39, Secondary 11J86, 11D61 |
| url | https://arxiv.org/abs/2405.15839 |