{
  "annotation_id": "02d4df2c-f650-46b5-aa03-26d04589ebdc",
  "date_created": "2026-02-17T05:53:12.309000Z",
  "date_modified": "2026-02-17T05:53:12.309000Z",
  "file_hash": "f9726b1f7e6bbbc3b3c74308acd1796a63b07f43c5f2ae636dcc98bce4a8a767",
  "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": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e7ad6e15-805d-44eb-b56d-b1ac9b6bc1f3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}