{"id":"https://openalex.org/W2023146651","doi":"https://doi.org/10.1007/s10998-009-9059-6","title":"On the family of diophantine triples {k + 1, 4k, 9k + 3}","display_name":"On the family of diophantine triples {k + 1, 4k, 9k + 3}","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2023146651","doi":"https://doi.org/10.1007/s10998-009-9059-6","mag":"2023146651"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-009-9059-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-009-9059-6","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","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/A5047770914","display_name":"Bo He","orcid":"https://orcid.org/0000-0002-2772-539X"},"institutions":[{"id":"https://openalex.org/I4210117337","display_name":"Neijiang Normal University","ror":"https://ror.org/02bc8tz70","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117337"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo He","raw_affiliation_strings":["Department of Mathematics Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, 641112, P. R. China","Neijiang Normal University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan, 641112, P. R. China","institution_ids":["https://openalex.org/I4210117337"]},{"raw_affiliation_string":"Neijiang Normal University","institution_ids":["https://openalex.org/I4210117337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067877694","display_name":"Alain Togb\u00e9","orcid":"https://orcid.org/0000-0002-5882-936X"},"institutions":[{"id":"https://openalex.org/I117015748","display_name":"Purdue University Northwest","ror":"https://ror.org/04keq6987","country_code":"US","type":"education","lineage":["https://openalex.org/I117015748"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alain Togb\u00e9","raw_affiliation_strings":["Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN, 46391, USA","Purdue University North Central,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN, 46391, USA","institution_ids":["https://openalex.org/I117015748"]},{"raw_affiliation_string":"Purdue University North Central,","institution_ids":["https://openalex.org/I117015748"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047770914"],"corresponding_institution_ids":["https://openalex.org/I4210117337"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.1828,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.75184074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"1","first_page":"59","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9991000294685364,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.91879802942276},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.8086162805557251},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.8000102043151855},{"id":"https://openalex.org/keywords/square-number","display_name":"Square number","score":0.7060257792472839},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6297799348831177},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4960688054561615},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4824603199958801},{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.4205821752548218},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.411737859249115},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3977583944797516},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.053794026374816895}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.91879802942276},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8086162805557251},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8000102043151855},{"id":"https://openalex.org/C173808221","wikidata":"https://www.wikidata.org/wiki/Q50705","display_name":"Square number","level":2,"score":0.7060257792472839},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6297799348831177},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4960688054561615},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4824603199958801},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.4205821752548218},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.411737859249115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3977583944797516},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.053794026374816895},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10998-009-9059-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-009-9059-6","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:187017","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309036","display_name":"Purdue University","ror":"https://ror.org/02dqehb95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W112603257","https://openalex.org/W204925304","https://openalex.org/W1541970503","https://openalex.org/W1837136997","https://openalex.org/W1975413201","https://openalex.org/W1994024219","https://openalex.org/W1994976559","https://openalex.org/W1995660901","https://openalex.org/W2024621281","https://openalex.org/W2031804978","https://openalex.org/W2035471152","https://openalex.org/W2039327237","https://openalex.org/W2044266254","https://openalex.org/W2048703701","https://openalex.org/W2063173539","https://openalex.org/W2068241246","https://openalex.org/W2068578745","https://openalex.org/W2074643817","https://openalex.org/W2076158618","https://openalex.org/W2087416278","https://openalex.org/W2092715653","https://openalex.org/W2144042597","https://openalex.org/W2146668962","https://openalex.org/W2148161807","https://openalex.org/W2297456208","https://openalex.org/W2596028034","https://openalex.org/W2791520396","https://openalex.org/W4239678843","https://openalex.org/W4256378823","https://openalex.org/W4285719527","https://openalex.org/W4403297239"],"related_works":["https://openalex.org/W4253945154","https://openalex.org/W2025770640","https://openalex.org/W2362414997","https://openalex.org/W217056885","https://openalex.org/W2889318194","https://openalex.org/W2363479010","https://openalex.org/W2386565732","https://openalex.org/W2389462200","https://openalex.org/W3215720862","https://openalex.org/W2150566934"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
