An Exponential Diophantine equation $x^2+3^α 113^β=y^{\mathfrak{n}}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911879027228672 |
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| author | Muthuvel, S. Venkatraman, R. |
| author_facet | Muthuvel, S. Venkatraman, R. |
| contents | The objective of the paper is to determine the complete solutions for the Diophantine equation $x^2 + 3^α113^β = y^{\mathfrak{n}}$ in positive integers $x$ and $y$ (where $x, y \geq 1$), non-negative exponents $α$ and $β$, and an integer $\mathfrak{n}\geq 3$, subject to the condition $\text{gcd}(x, y) = 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_09252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Exponential Diophantine equation $x^2+3^α 113^β=y^{\mathfrak{n}}$ Muthuvel, S. Venkatraman, R. Number Theory 11D41, 11D61, 11Y50 The objective of the paper is to determine the complete solutions for the Diophantine equation $x^2 + 3^α113^β = y^{\mathfrak{n}}$ in positive integers $x$ and $y$ (where $x, y \geq 1$), non-negative exponents $α$ and $β$, and an integer $\mathfrak{n}\geq 3$, subject to the condition $\text{gcd}(x, y) = 1$. |
| title | An Exponential Diophantine equation $x^2+3^α 113^β=y^{\mathfrak{n}}$ |
| topic | Number Theory 11D41, 11D61, 11Y50 |
| url | https://arxiv.org/abs/2405.09252 |