Diophantine equations involving powers of factorials
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916964292624384 |
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| author | Novaković, Saša |
| author_facet | Novaković, Saša |
| contents | We are motivated by a result of Alzer and Luca who presented all the integer solutions to the relations $(k!)^n-k^n=(n!)^k-n^k$ and $(k!)^n+k^n=(n!)^k+n^k$. We consider the equations $(k!)^{n!}\pm k^n=(n!)^{k!}\pm n^k$ and $(k!)^n\pm k^{n!}=(n!)^k\pm n^{k!}$ and prove a similar statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diophantine equations involving powers of factorials Novaković, Saša Number Theory 11A25, 11A41, 11D99 We are motivated by a result of Alzer and Luca who presented all the integer solutions to the relations $(k!)^n-k^n=(n!)^k-n^k$ and $(k!)^n+k^n=(n!)^k+n^k$. We consider the equations $(k!)^{n!}\pm k^n=(n!)^{k!}\pm n^k$ and $(k!)^n\pm k^{n!}=(n!)^k\pm n^{k!}$ and prove a similar statement. |
| title | Diophantine equations involving powers of factorials |
| topic | Number Theory 11A25, 11A41, 11D99 |
| url | https://arxiv.org/abs/2509.18860 |