{
  "annotation_id": "9808aceb-4feb-4367-868d-9dd229d6a4cf",
  "date_created": "2026-02-17T05:53:11.948000Z",
  "date_modified": "2026-02-17T05:53:11.948000Z",
  "file_hash": "639ab2115cdd3c7f2f6eaa5dd2551112ec13c3fa777a50e0894775e9d55b3e80",
  "private": false,
  "record": {
    "abstract": "We show that there are $O(B^{3/5-3/1555+\\ep})$ triples $(x,y,z)$ of square-full integesr up to $B$ satisfying the equation $x+y=z$ for any fixed $\\ep\u003e0$. This is the first improvement over the `easy\u0027 exponent $3/5$, given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations $aX^3+bY^3=cZ^3$.",
    "arxiv_id": "2601.07817",
    "authors": [
      "D. R. Heath-Brown"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Counting Square-full Solutions to $x+y=z$",
    "url": "https://arxiv.org/abs/2601.07817",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a33fd7b2-06ad-4dae-8b6d-cfb6be539887",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}