{"?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-U7TDJLJG/deb56ceb-f38e-4545-b916-1172e57caacc/PDF","dcterms:extent":"278 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-U7TDJLJG/b951cb67-1b0e-44db-99c8-7525a81b7bee/TEXT","dcterms:extent":"33 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-U7TDJLJG","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":"Casacuberta, Sílvia","dc:format":[{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 297-309"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:44726019","URN:URN:NBN:SI:doc-U7TDJLJG"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"binomial coefficients"},{"@xml:lang":"sl","#text":"binomski koeficienti"},{"@xml:lang":"sl","#text":"deljivost"},{"@xml:lang":"en","#text":"divisibility"},{"@xml:lang":"en","#text":"primorials"},{"@xml:lang":"sl","#text":"primoriel"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the divisibility of binomial coefficients|"},"dc:description":[{"@xml:lang":"sl","#text":"Shareshian and Woodroofe asked if for every positive integer ?$n$? there exist primes ?$p$? and ?$q$? such that, for all integers ?$k$? with ?$1 \\le k \\le n-1$?, the binomial coefficient ?$\\binom{n}{k}$? is divisible by at least one of ?$p$? or ?$q$?. We give conditions under which a number ?$n$? has this property and discuss a variant of this problem involving more than two primes. We prove that every positive integer ?$n$? has infinitely many multiples with this property"},{"@xml:lang":"sl","#text":"Shareshian in Woodroofe sta vprašala, če za poljubno pozitivno celo število ?$n$? obstajata taki praštevili ?$p$? in ?$q$?, da je za vsa cela števila ?$k$?, za katera velja ?$1 \\le k \\le n-1$?, binomski koeficient ?$\\binom{n}{k}$? deljiv vsaj z enim od ?$p$? ali ?$q$?. V prispevku podamo pogoje, ki jih mora zadoščati ?$n$? s to lastnostjo, in obravnavamo različice tega problema za več kot dve praštevili. Med drugim dokažemo, da ima vsako naravno število ?$n$? neskončno mnogo večkratnikov s to lastnostjo"}],"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-U7TDJLJG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-U7TDJLJG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-U7TDJLJG/deb56ceb-f38e-4545-b916-1172e57caacc/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"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":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-U7TDJLJG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-U7TDJLJG"}}}}