The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909705789505536 |
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| author | He, Bo Liu, Chang |
| author_facet | He, Bo Liu, Chang |
| contents | In this paper, we investigate the Diophantine equation \[ (2^k - 1)(3^k - 1) = x^n \] and prove that it has no solutions in positive integers $k, x, n > 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$ He, Bo Liu, Chang Number Theory 11D41 In this paper, we investigate the Diophantine equation \[ (2^k - 1)(3^k - 1) = x^n \] and prove that it has no solutions in positive integers $k, x, n > 2$. |
| title | The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$ |
| topic | Number Theory 11D41 |
| url | https://arxiv.org/abs/2501.04050 |