{"id":"https://openalex.org/W7131350582","doi":"https://doi.org/10.1051/ita/2026003","title":"A system of two Diophantine inequalities with primes","display_name":"A system of two Diophantine inequalities with primes","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7131350582","doi":"https://doi.org/10.1051/ita/2026003"},"language":null,"primary_location":{"id":"doi:10.1051/ita/2026003","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2026003","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2026/01/ita20250094.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.rairo-ita.org/articles/ita/pdf/2026/01/ita20250094.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126762835","display_name":"Yanjun Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanjun Dong","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016281551","display_name":"Qian Wang","orcid":"https://orcid.org/0000-0002-8822-6017"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qian Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016281551"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33944418,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":null,"first_page":"3","last_page":"3"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4512999951839447,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4512999951839447,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.30169999599456787,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0746999979019165,"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/diophantine-equation","display_name":"Diophantine equation","score":0.6266999840736389},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5400000214576721},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.460099995136261},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.40560001134872437},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.383899986743927},{"id":"https://openalex.org/keywords/diophantine-set","display_name":"Diophantine set","score":0.3799999952316284},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.37610000371932983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465999722480774},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.6266999840736389},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4763000011444092},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.460099995136261},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41990000009536743},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.3799999952316284},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28519999980926514},{"id":"https://openalex.org/C171223647","wikidata":"https://www.wikidata.org/wiki/Q207264","display_name":"Fermat number","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C173808221","wikidata":"https://www.wikidata.org/wiki/Q50705","display_name":"Square number","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C555856410","wikidata":"https://www.wikidata.org/wiki/Q65122107","display_name":"Diophantine geometry","level":4,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ita/2026003","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2026003","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2026/01/ita20250094.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ita/2026003","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/2026003","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2026/01/ita20250094.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8301432854","display_name":null,"funder_award_id":"12171286","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7131350582.pdf","grobid_xml":"https://content.openalex.org/works/W7131350582.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1012819894","https://openalex.org/W1986769339","https://openalex.org/W1992674904","https://openalex.org/W2053846678","https://openalex.org/W2333904902","https://openalex.org/W2944822968","https://openalex.org/W2946995869","https://openalex.org/W2990488786","https://openalex.org/W3106110752","https://openalex.org/W3131412916","https://openalex.org/W3215742235"],"related_works":[],"abstract_inverted_index":{"Let":[0],"k":[1,10,13,29,100,123,144],"\u2265":[2],"7":[3],"be":[4],"fixed,":[5],"and":[6,32,58,75],"v":[7,21,42],"=":[8],"(55":[9],"+":[11,14,96,98,119,121],"556)/(26":[12],"672),1":[15],"<":[16,18,20,24,26,28,106,129],"d":[17,118,124],"c":[19,95,101],",":[22,49,62,114],"1":[23,39,48,61,70,74,94,104,108,113,117,141],"\u03bc":[25,33],"\u03bd":[27],"1\u2212":[30],"d/c":[31,40],"\u2264":[34,41],"N":[35,38,46,50,60,63,69,72,76,79,103,107,112,126,130,135],"2":[36,52,64,77,81,127,131,136],"/":[37],".":[43,82,145],"Suppose":[44],"that":[45,59],"\u2032":[47,51,73,80],">":[53,71,78],"0":[54],"are":[55,65],"real":[56,66],"numbers,":[57],"numbers":[67],"satisfying":[68],"Then":[83],"we":[84],"prove":[85],"the":[86],"system":[87],"of":[88],"two":[89],"Diophantine":[90],"inequalities":[91],"|":[92,105,115,128],"p":[93,99,116,122,140,143],"\u2026":[97,120],"\u2212":[102,125],"\u2212(1/c)(v\u2212c)":[109],"log":[110,133],"195":[111,134],"\u2212(1/d)(v\u2212d)":[132],"has":[137],"prime":[138],"solutions":[139],",\u2026,":[142]},"counts_by_year":[],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2026-02-25T00:00:00"}