{
  "abstract": "We prove that every positive rational number is a sum of distinct unit fractions with denominators of the form $g-h$, where $g$ is a Golomb prime and $h$ is a fixed nonzero integer, as long as the necessary congruence conditions are satisfied. Golomb primes, introduced by Golomb in 1955, are a natural analogue of the primes. Erdős showed that the relative density of Golomb primes among the primes up to $N$ is about $1/\\log\\log N$, so they form a sparse subset of the primes. Our result is an analogue of Bloom's result on unit fraction representations using shifted primes, for this sparse subset of the primes. A key ingredient in our proof is a Siegel--Walfisz-type theorem for Golomb primes in arithmetic progressions, which we also prove here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06798",
  "author_total": 1,
  "authors": [
    {
      "name": "Rishika Agrawal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x278qbx1varq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06798",
  "fulltext_url": null,
  "id": "6x278qbx1varq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06798",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x278qbx1varq.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Unit fraction representations using shifted Golomb primes",
  "title_text": "Unit fraction representations using shifted Golomb primes",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/6x278qbx1varq",
  "venue": "arXiv",
  "versions": []
}