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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13867 |
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Table of Contents:
- Let $S_l(M,N)$ denote a set of $\ell$ triples of positive integers having the same sum $M$ and the same product $N$. For each $2\leq\ell\leq 4$ we establish a connection between a subset of $S_l(M,N)$ with (integral) parametric elements and a family of elliptic curves. When $\ell=2$ and $3$, we use certain known subsets of $S_l(M,N)$ with parametric elements and respectively find families of elliptic curves of generic rank $\geq 5$ and $\geq 6$, while for $\ell=4$ we first obtain a subset of $S_l(M,N)$ with parametric elements, then construct a family of elliptic curves of generic rank $\geq 8$. Finally, we perform a computer search within these families to find specific curves with rank $\geq 11$ and in particular we found two curves of rank $14$.