Two dimensional covering systems and possible prime producing $a^m-b^n$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914464416137216 |
|---|---|
| author | Granville, Andrew Pappalardi, Francesco |
| author_facet | Granville, Andrew Pappalardi, Francesco |
| contents | We exhibit a new application of two dimensional covering systems, examples of integer pairs $a,b$ for which $a^m-b^n$ has a prime divisor from some given finite set of primes, for every pair of integers $m,n\geq 0$. This leads us to conjecture what are the only possible obstructions to $|a^m-b^n|$ taking on infinitely many distinct prime values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10296 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two dimensional covering systems and possible prime producing $a^m-b^n$ Granville, Andrew Pappalardi, Francesco Number Theory 11A41 We exhibit a new application of two dimensional covering systems, examples of integer pairs $a,b$ for which $a^m-b^n$ has a prime divisor from some given finite set of primes, for every pair of integers $m,n\geq 0$. This leads us to conjecture what are the only possible obstructions to $|a^m-b^n|$ taking on infinitely many distinct prime values. |
| title | Two dimensional covering systems and possible prime producing $a^m-b^n$ |
| topic | Number Theory 11A41 |
| url | https://arxiv.org/abs/2601.10296 |