{"id":"https://openalex.org/W4414313122","doi":"https://doi.org/10.1080/00029890.2025.2540755","title":"A Polynomial with a Root Mod <i>p</i> for Every <i>p</i> has a Real Root","display_name":"A Polynomial with a Root Mod <i>p</i> for Every <i>p</i> has a Real Root","publication_year":2025,"publication_date":"2025-09-18","ids":{"openalex":"https://openalex.org/W4414313122","doi":"https://doi.org/10.1080/00029890.2025.2540755"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2025.2540755","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2540755","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075625262","display_name":"Rodrigo Angelo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rodrigo Angelo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044509754","display_name":"Max Wenqiang Xu","orcid":"https://orcid.org/0000-0002-4964-0186"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max Wenqiang Xu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4964-0186","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35641105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"132","issue":"9","first_page":"918","last_page":"925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mod","display_name":"Mod","score":0.8414000272750854},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.7591999769210815},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5389000177383423},{"id":"https://openalex.org/keywords/root-finding-algorithm","display_name":"Root-finding algorithm","score":0.36890000104904175},{"id":"https://openalex.org/keywords/reciprocal-polynomial","display_name":"Reciprocal polynomial","score":0.3190999925136566}],"concepts":[{"id":"https://openalex.org/C29231244","wikidata":"https://www.wikidata.org/wiki/Q865493","display_name":"Mod","level":2,"score":0.8414000272750854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8349000215530396},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.7591999769210815},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4537000060081482},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.36890000104904175},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.3190999925136566},{"id":"https://openalex.org/C6026789","wikidata":"https://www.wikidata.org/wiki/Q948010","display_name":"Primitive root modulo n","level":3,"score":0.30320000648498535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30219998955726624},{"id":"https://openalex.org/C107775665","wikidata":"https://www.wikidata.org/wiki/Q12859399","display_name":"Properties of polynomial roots","level":4,"score":0.2833000123500824},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2025.2540755","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2540755","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W606794057","https://openalex.org/W1570243798","https://openalex.org/W2007704176","https://openalex.org/W2062708552","https://openalex.org/W2132287244","https://openalex.org/W2400130777","https://openalex.org/W3129355156","https://openalex.org/W4240694056","https://openalex.org/W4281704411"],"related_works":[],"abstract_inverted_index":{"We":[0,25],"prove":[1],"that":[2,52],"if":[3],"a":[4,10,22],"polynomial":[5],"with":[6,27],"rational":[7],"coefficients":[8],"has":[9,21],"root":[11],"mod":[12,40],"p":[13],"for":[14],"every":[15],"large":[16],"prime":[17],"p,":[18,41],"then":[19],"it":[20],"real":[23],"root.":[24],"show":[26,51],"examples":[28],"how":[29],"to":[30,35,44],"use":[31],"Chebotarev\u2019s":[32],"density":[33],"theorem":[34],"study":[36],"roots":[37],"of":[38],"polynomials":[39],"leading":[42],"up":[43],"our":[45],"proof.":[46],"As":[47],"an":[48],"application,":[49],"we":[50],"the":[53],"primes":[54],"can\u2019t":[55],"be":[56],"covered":[57],"by":[58],"finitely":[59],"many":[60],"positive":[61],"definite":[62],"binary":[63],"quadratic":[64],"forms.":[65]},"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
