Two dimensional covering systems and possible prime producing $a^m-b^n$
Abstract
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.
Fields of Study & Subjects
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Limits and Structures in Graph Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint