| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Lepp\u00e4l\u00e4, Emma", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Aho, Vieno", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2022-09-28T05:33:20Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2022-09-28T05:33:20Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2022", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/83331", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n tutkielman aiheena on alkulukutestit, jotka ovat sellaisia menetelmi\u00e4 ja algoritmeja, joiden avulla voidaan tutkia, onko jokin luku alkuluku vai alkulukujen tulo. Tutkielman alussa k\u00e4yd\u00e4\u00e4n l\u00e4pi joitakin yksinkertaisia m\u00e4\u00e4ritelmi\u00e4 ja aputuloksia jaollisuuteen liittyen sek\u00e4 Eratostheneen seula, jonka avulla voidaan etsi\u00e4 pienempi\u00e4 alkulukuja. Toisessa luvussa k\u00e4yd\u00e4\u00e4n l\u00e4pi joitakin kongruenssiin liittyvi\u00e4 tuloksia, joita tarvitaan my\u00f6hemminkin tutkielmassa. Toisessa luvussa osoitetaan my\u00f6s Fermat'n pieni lause ja Wilsonin lause, joiden avulla voidaan tutkia hieman suurempienkin lukujen jaollisuutta.\n\nTutkielman ensimm\u00e4inen p\u00e4\u00e4tulos on probabilistinen Solovay-Strassenin alkulukutesti. Se antaa todenn\u00e4k\u00f6isen vastauksen, onko tutkittava luku alkuluku. T\u00e4t\u00e4 testi\u00e4 varten kolmannen luvun alussa osoitetaan erilaisia tuloksia sek\u00e4 lukuteorian ett\u00e4 my\u00f6s algebran osa-alueilta. Lis\u00e4ksi luvussa tutustutaan erilaisten pseudoalkulujen k\u00e4sitteisiin ja osoitetaan niihin liittyvi\u00e4 aputuloksia, ennen kuin voidaan varsinaisesti k\u00e4sitell\u00e4 Solovay-Strassenin alkulukutesti\u00e4.\n\nToinen p\u00e4\u00e4tulos on deterministinen Miller-Rabinin alkulukutesti. Se antaa varman vastauksen, onko tutkittava luku alkuluku. T\u00e4t\u00e4 testi\u00e4 varten on nelj\u00e4nnen luvun alussa j\u00e4lleen aputuloksia, joita tarvitaan Miller-Rabinin alkulukutestin k\u00e4sittelyyn. Tutkielman viidenness\u00e4 luvussa esitell\u00e4\u00e4n viel\u00e4 alkulukutestien sovelluksena RSA-salausmenetelm\u00e4, johon alkulukutestej\u00e4 voidaan hy\u00f6dynt\u00e4\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2022-09-28T05:33:19Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2022-09-28T05:33:20Z (GMT). No. of bitstreams: 0\n Previous issue date: 2022", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "55", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Alkulukutestej\u00e4", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202209284686", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "alkuluvut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "lukuteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "luvut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "diskreetti matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
|