{
  "abstract": "We show that for every uniform family of affine algebraic sets, there is a formula in the parameters of the family and in $n$, expressing the cardinality of the set in the ring $\\mathbb Z/n \\mathbb Z$. In particular, we construct such a formula for the elliptic curves in Weierstrass normal form. These formulas are arithmetic terms: fixed finite compositions of additions, multiplications, subtractions, divisions with remainder and integer exponentiations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22049",
  "author_total": 1,
  "authors": [
    {
      "name": "Mihai Prunescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bk8z6pc0sd3ps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22049",
  "fulltext_url": null,
  "id": "bk8z6pc0sd3ps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22049",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204163554",
  "pdf_url": "https://arxiv.org/pdf/2608.22049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bk8z6pc0sd3ps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2608.22049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "How many points does an affine algebraic set have in residue classes modulo n ?",
  "title_text": "How many points does an affine algebraic set have in residue classes modulo n ?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/bk8z6pc0sd3ps",
  "venue": "arXiv",
  "versions": []
}