{"id":"https://openalex.org/W4390622020","doi":"https://doi.org/10.2478/forma-2023-0022","title":"Elementary Number Theory Problems. Part XII \u2013 Primes in Arithmetic Progression","display_name":"Elementary Number Theory Problems. Part XII \u2013 Primes in Arithmetic Progression","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4390622020","doi":"https://doi.org/10.2478/forma-2023-0022"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2023-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0022","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0022","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2023-0022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073856205","display_name":"Adam Grabowski","orcid":"https://orcid.org/0000-0001-5026-3990"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Adam Grabowski","raw_affiliation_strings":["Faculty of Computer Science University of Bia\u0142ystok Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science University of Bia\u0142ystok Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073856205"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":20.4514,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.99280945,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"277","last_page":"286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12504","display_name":"Mathematics and Applications","score":0.9804999828338623,"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/T13500","display_name":"Probability and Statistical Research","score":0.9575999975204468,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.7147046327590942},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.666832447052002},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5912657976150513},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.5682876110076904},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.46635404229164124},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4366888999938965},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3588246703147888},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15063580870628357}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7147046327590942},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.666832447052002},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5912657976150513},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.5682876110076904},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.46635404229164124},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4366888999938965},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3588246703147888},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15063580870628357},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2023-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0022","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0022","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/15860","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/15860","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/15860/1/Elementary-Number-Theory-Problems-Part-XII-Primes-in-Arithmetic-Progression.pdf","source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2023-0022","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0022","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0022","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390622020.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1625130818","https://openalex.org/W2268053682","https://openalex.org/W2480281325","https://openalex.org/W3042429209","https://openalex.org/W4244921654","https://openalex.org/W4253418349","https://openalex.org/W4280648536","https://openalex.org/W4313308188","https://openalex.org/W4313308209","https://openalex.org/W4386297760"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2952002389","https://openalex.org/W2231510842","https://openalex.org/W3106363734","https://openalex.org/W1969707919","https://openalex.org/W2577553587","https://openalex.org/W2053314506","https://openalex.org/W2166647448","https://openalex.org/W1518783954","https://openalex.org/W2018276851"],"abstract_inverted_index":{"Summary":[0],"In":[1],"this":[2],"paper":[3],"another":[4],"twelve":[5],"problems":[6],"from":[7],"W.":[8],"Sierpi\u0144ski\u2019s":[9],"book":[10],"\u201c250":[11],"Problems":[12],"in":[13],"Elementary":[14],"Number":[15],"Theory\u201d":[16],"are":[17],"formalized,":[18],"using":[19],"the":[20,38],"Mizar":[21],"formalism,":[22],"namely:":[23],"42,":[24],"43,":[25],"51,":[26],"51a,":[27],"57,":[28],"59,":[29],"72,":[30],"135,":[31],"136,":[32],"and":[33],"153\u2013155.":[34],"Significant":[35],"amount":[36],"of":[37],"work":[39],"is":[40],"devoted":[41],"to":[42],"arithmetic":[43],"progressions.":[44]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
