{
  "abstract": "We apply the notion of \\emph{olloid} to show that the family of Erd\\H{o}s-Straus-type equations $$ \\frac{4^{2^l}}{n^{2^l}}=\\frac{1}{x^{2^l}}+\\frac{1}{y^{2^l}}+\\frac{1}{z^{2^l}} $$ has solutions for all $l\\geq 1$ provided that the equation $$ \\frac{4}{n}=\\frac{1}{x}+\\frac{1}{y}+\\frac{1}{z} $$ has a solution for a fixed $n>4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Theophilus Agama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cc25twnj7b3dj.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "cc25twnj7b3dj",
  "issns": [],
  "landing_url": "https://hal.science/hal-05766100v1",
  "language": "en",
  "licence": "CC-BY-ND-4.0",
  "licence_label": "CC BY-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05766100/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cc25twnj7b3dj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05766100",
      "source": "hal",
      "url": "https://hal.science/hal-05766100v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "ON THE EXISTENCE OF SOLUTIONS TO ERDŐS-STRAUS TYPE EQUATIONS",
  "title_text": "ON THE EXISTENCE OF SOLUTIONS TO ERDŐS-STRAUS TYPE EQUATIONS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/cc25twnj7b3dj",
  "venue": "HAL",
  "versions": []
}