{
  "annotation_id": "c24e15d5-4ff4-47f5-bb86-d3d57ce05c69",
  "date_created": "2026-02-17T05:53:12.653000Z",
  "date_modified": "2026-02-17T05:53:12.653000Z",
  "file_hash": "6fb95a0ce7bb708f57587f812ca6bcb95883db1c55df018f3cdd67ac356bd9f4",
  "private": false,
  "record": {
    "abstract": "We settle an open problem regarding palindromes; that is, positive integers which are the same when written forwards and backwards. In particular, we prove that for any fixed base $b\\geq 2$, there exist infinitely many square-free palindromes in base $b$. We also provide an asymptotic expression for the number of such integers $\\leq x$. The core of our proof utilises a hybrid $p$-adic/Archimedean van der Corput process, used in conjunction with an equidistribution estimate of Tuxanidy and Panario, as well as an elementary argument of Cilleruelo, Luca and Shparlinski.",
    "arxiv_id": "2601.07097",
    "authors": [
      "Daniel R. Johnston",
      "Bryce Kerr"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The infinitude of square-free palindromes",
    "url": "https://arxiv.org/abs/2601.07097",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5a469457-403a-4c6c-acaa-cc92d10dd714",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}