On the representation of number-theoretic functions by arithmetic terms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916328738127872 |
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| author | Prunescu, Mihai Sauras-Altuzarra, Lorenzo |
| author_facet | Prunescu, Mihai Sauras-Altuzarra, Lorenzo |
| contents | We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors function, Euler's totient function, the modular inverse, the integer part of the root, the integer part of the logarithm, the multiplicative order and the discrete logarithm. Although these are very complicated, they only involve elementary operations, and to our knowledge no other closed form of this kind is known for the aforementioned functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12928 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the representation of number-theoretic functions by arithmetic terms Prunescu, Mihai Sauras-Altuzarra, Lorenzo Number Theory 11A25, 03D20 We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors function, Euler's totient function, the modular inverse, the integer part of the root, the integer part of the logarithm, the multiplicative order and the discrete logarithm. Although these are very complicated, they only involve elementary operations, and to our knowledge no other closed form of this kind is known for the aforementioned functions. |
| title | On the representation of number-theoretic functions by arithmetic terms |
| topic | Number Theory 11A25, 03D20 |
| url | https://arxiv.org/abs/2407.12928 |