Article Instance

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{
    "pk": 59052,
    "title": "On the Applications of Cyclotomic Fields in Introductory Number Theory",
    "subtitle": null,
    "abstract": "In this essay, we study and comment on two number theoretical applications on prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime). We begin by giving a simplified proof of Kummer's case of Fermat's Last Theorem obtained by linking different versions of the proof in different textbooks. We finally modernize Dirichlet's solution to Pell's Equation.",
    "language": "en",
    "license": null,
    "keywords": [
        {
            "word": "Number Theory"
        },
        {
            "word": "Cyclotomic Fields"
        },
        {
            "word": "Pell's Equation"
        },
        {
            "word": "Dirichlet"
        },
        {
            "word": "Kummer"
        },
        {
            "word": "Fermat's Last Theorem"
        },
        {
            "word": "Primary Units"
        },
        {
            "word": "Real Units"
        },
        {
            "word": "mathematics"
        }
    ],
    "section": "Research",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/49c0561x",
    "frozenauthors": [
        {
            "first_name": "Kabalan",
            "middle_name": "",
            "last_name": "Gaspard",
            "name_suffix": "",
            "institution": "Mathematical Institute, Oxford University",
            "department": ""
        }
    ],
    "date_submitted": "2013-03-05T03:50:05Z",
    "date_accepted": "2013-03-05T03:50:05Z",
    "date_published": "2013-03-04T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/our_bsj/article/59052/galley/45089/download/"
        }
    ]
}