Fermat Numbers: Pseudoprimality and Primality Constraints
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918472786640896 |
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| author | Starni, Paolo |
| author_facet | Starni, Paolo |
| contents | We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent $(F_n-1)/4$. Moreover, in connection with Pépin's primality test, we obtain a characterization of pseudoprimality to the base $3$ (and, more generally, to other Pépin-admissible bases). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fermat Numbers: Pseudoprimality and Primality Constraints Starni, Paolo General Mathematics 11A51, 11A07 We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent $(F_n-1)/4$. Moreover, in connection with Pépin's primality test, we obtain a characterization of pseudoprimality to the base $3$ (and, more generally, to other Pépin-admissible bases). |
| title | Fermat Numbers: Pseudoprimality and Primality Constraints |
| topic | General Mathematics 11A51, 11A07 |
| url | https://arxiv.org/abs/2604.25973 |