{
  "abstract": "We prove an equidistribution theorem for numbers with all-nonzero decimal digits and prescribed digit sum and residue class. As a corollary, we resolve Murthy's conjecture (OEIS A077754, 2002): an integer n admits a multiple with at least two nonzero digits and digit sum n iff n is not in {1, 2, 5, 11} ∪ 10ℕ. The corollary is fully machine-verified in Lean 4 with mathlib (theorem A077754, zero sorry). The deposit includes the paper (paper.pdf), the complete Lean formalization (A077754.lean, CornerTable.lean), an independent Python verifier (~90 lines, stdlib) re-deriving all finite certificates, and the pinned build files (lakefile.toml, lake-manifest.json, lean-toolchain) for long-term reproducibility.",
  "abstract_shown": true,
  "affiliations": [
    "University of Caen"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Frédéric Gaudin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jwf7wb3p38rw.bib",
  "cited_by": 6,
  "doi": "10.5281/zenodo.23879087",
  "fulltext_url": null,
  "id": "7jwf7wb3p38rw",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.23879087",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7225111083",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/7jwf7wb3p38rw.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T13:20:22Z",
      "native_id": "W7225111083",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23879087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Prescribed digit sums in residue classes and a conjecture of Murthy (OEIS A077754)",
  "title_text": "Prescribed digit sums in residue classes and a conjecture of Murthy (OEIS A077754)",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/7jwf7wb3p38rw",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}