{
  "annotation_id": "0677bd79-9d80-4a71-b52a-aa14fadc1603",
  "date_created": "2026-02-17T05:53:24.293000Z",
  "date_modified": "2026-02-17T05:53:24.293000Z",
  "file_hash": "4c2721c6d5408c27c83baff6ba7b061f52120716a36efca0408aa614ce16913d",
  "private": false,
  "record": {
    "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.",
    "arxiv_id": "2601.10296",
    "authors": [
      "Andrew Granville",
      "Francesco Pappalardi"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Two dimensional covering systems and possible prime producing $a^m-b^n$",
    "url": "https://arxiv.org/abs/2601.10296",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a5fdaaec-69fa-43b3-9255-d6259a720da8",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}