{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CYSBZTCU/28f48039-36df-4660-9817-bf1c424a1e57/PDF","dcterms:extent":"255 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CYSBZTCU/efaa7d67-0142-4c6e-a8b4-78c584029687/TEXT","dcterms:extent":"0 KB"}],"edm:TimeSpan":{"@rdf:about":"2012-2024","edm:begin":{"@xml:lang":"en","#text":"2012"},"edm:end":{"@xml:lang":"en","#text":"2024"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-CYSBZTCU","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-XHBM81BF"},{"@xml:lang":"sl","#text":"Matematika v šoli"}],"dcterms:issued":"2013","dc:creator":"Jerman, Marjan","dc:format":[{"@xml:lang":"sl","#text":"številka:1/2"},{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"str. 54-60"}],"dc:identifier":["ISSN:1318-010X","COBISSID:16716889","URN:URN:NBN:SI:doc-CYSBZTCU"],"dc:language":"sl","dc:publisher":[{"@xml:lang":"sl","#text":"Zavod Republike Slovenije za šolstvo"},{"@xml:lang":"sl","#text":"Zavod Republike Slovenije za šolstvo in šport"}],"dc:subject":[{"@xml:lang":"sl","#text":"Bezoutova identiteta"},{"@xml:lang":"en","#text":"Bézout's identity"},{"@xml:lang":"en","#text":"Chinese remainder theorem"},{"@xml:lang":"en","#text":"continued fractions"},{"@xml:lang":"en","#text":"Euclidean algorithm"},{"@xml:lang":"en","#text":"Euclidean domain"},{"@xml:lang":"sl","#text":"Evklidov algoritem"},{"@xml:lang":"sl","#text":"evklidski kolobar"},{"@xml:lang":"en","#text":"history of mathematics"},{"@xml:lang":"sl","#text":"kitajski izrek o ostankih"},{"@xml:lang":"en","#text":"linear Diophantine equations"},{"@xml:lang":"sl","#text":"linearne diofantske enačbe"},{"@xml:lang":"sl","#text":"Pellova enačba"},{"@xml:lang":"en","#text":"Pell's equation"},{"@xml:lang":"sl","#text":"verižni ulomki"},{"@xml:lang":"sl","#text":"zgodovina matematike"}],"dcterms:temporal":{"@rdf:resource":"2012-2024"},"dc:title":{"@xml:lang":"sl","#text":"Evklidov algoritem| Euclidean algorithm|"},"dc:description":[{"@xml:lang":"sl","#text":"The article briefly describes the history of Euclidean algorithm. Described within are some classical methods of its use in the theory of numbers: Bézout's identity, solving linear Diophantine equations, its application on the Chinese remainder theorem, approximation of the roots of natural numbers with help of continued fractions, and solving Pell's equation. The article concludes with a generalization based on Euclidean domains, mentioning the domains of polynomials in one variable with coefficients from a division ring, Gaussian integers and Eisenstein integers"},{"@xml:lang":"sl","#text":"V prispevku je na kratko opisana zgodovina Evklidovega algoritma. Navedene so nekatere njegove klasične uporabe v teoriji števil: Bezoutova identiteta, reševanje linearnih diofantskih enačb, uporaba pri kitajskem izreku o ostankih, aproksimacija korenov naravnih števil z verižnimi ulomki in reševanje Pellove enačbe. Prispevek se konča s posplošitvijo na evklidske kolobarje, kjer so omenjeni kolobarji polinomov v eni spremenljivki s koeficienti iz komutativnega obsega, Gaussova števila in Eisensteinova števila"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-CYSBZTCU","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-CYSBZTCU"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-CYSBZTCU/28f48039-36df-4660-9817-bf1c424a1e57/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Zavod RS za šolstvo"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-CYSBZTCU/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-CYSBZTCU"}}}}