Products of factorials which are products of factorials
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915822064107520 |
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| author | Novaković, Saša |
| author_facet | Novaković, Saša |
| contents | In this note, we look at the diophantine equation
$$
\prod_{i=1}^ta_i!=\prod_{j=1}^sn_i!, \quad n_1\geq \cdots \geq n_s\geq 2 \quad \textnormal{and}\quad n_1>a_1\geq a_2\geq\cdots \geq a_t\geq2.
$$
\noindent
Let $s<t$. Under the (explicit) abc conjecture, we show that it has only finitely many nontrivial solutions in a certain subset of $\mathbb{N}^{t+s}$ of positive asymptotic density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23838 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Products of factorials which are products of factorials Novaković, Saša Number Theory 11D45, 11D72, 11D57 In this note, we look at the diophantine equation $$ \prod_{i=1}^ta_i!=\prod_{j=1}^sn_i!, \quad n_1\geq \cdots \geq n_s\geq 2 \quad \textnormal{and}\quad n_1>a_1\geq a_2\geq\cdots \geq a_t\geq2. $$ \noindent Let $s<t$. Under the (explicit) abc conjecture, we show that it has only finitely many nontrivial solutions in a certain subset of $\mathbb{N}^{t+s}$ of positive asymptotic density. |
| title | Products of factorials which are products of factorials |
| topic | Number Theory 11D45, 11D72, 11D57 |
| url | https://arxiv.org/abs/2602.23838 |