On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914266351665152 |
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| author | Kiss, Sándor Z. Sándor, Csaba Zakarczemny, Maciej |
| author_facet | Kiss, Sándor Z. Sándor, Csaba Zakarczemny, Maciej |
| contents | We consider the equality of the values of the $n$th and $k$th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$, we prove that this equation always has a solution, but only finitely many solutions. Furthermore, we consider the equality of the values of the $n$th and $(n-2)$th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. In particular, we show that the number of solutions of this equation tends to infinity if $n$ tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity Kiss, Sándor Z. Sándor, Csaba Zakarczemny, Maciej Number Theory We consider the equality of the values of the $n$th and $k$th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$, we prove that this equation always has a solution, but only finitely many solutions. Furthermore, we consider the equality of the values of the $n$th and $(n-2)$th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. In particular, we show that the number of solutions of this equation tends to infinity if $n$ tends to infinity. |
| title | On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.14057 |