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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.21757 |
| Etiquetas: |
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- This paper proves a conjecture proposed by Ren and Li (2015: 393, \emph{Journal of Inequalities and Applications}). Our result eliminates the constraints on the parity and size of $m$, as well as the restriction $x > 1$, required in Ren and Li's theorem. Consequently, it fully subsumes their results while extending validity to all integers $m \geq 1$ and all $x > 0$. Crucially, we establish the inequality $S_m(x) > σ_m(x)$ unconditionally, requiring no parity conditions, size conditions on $m$, or lower bound on $x$.