{"id":"https://openalex.org/W2551228764","doi":"https://doi.org/10.1007/s10998-016-0173-9","title":"On the number of positive integer solutions (x,\u00a0n) of the generalized Ramanujan\u2013Nagell equation $$x^2-2^r=p^n$$ x 2 - 2 r = p n","display_name":"On the number of positive integer solutions (x,\u00a0n) of the generalized Ramanujan\u2013Nagell equation $$x^2-2^r=p^n$$ x 2 - 2 r = p n","publication_year":2016,"publication_date":"2016-11-22","ids":{"openalex":"https://openalex.org/W2551228764","doi":"https://doi.org/10.1007/s10998-016-0173-9","mag":"2551228764"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-016-0173-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-016-0173-9","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/A5101748732","display_name":"Tingting Wang","orcid":"https://orcid.org/0000-0002-3691-2576"},"institutions":[{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tingting Wang","raw_affiliation_strings":["College of Science, Northwest A&F University, Yangling, 712100, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Science, Northwest A&F University, Yangling, 712100, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I89652312"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006703234","display_name":"Yingzhao Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingzhao Jiang","raw_affiliation_strings":["College of Science, Northwest A&F University, Yangling, 712100, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Science, Northwest A&F University, Yangling, 712100, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I89652312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101748732"],"corresponding_institution_ids":["https://openalex.org/I89652312"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.20728622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"75","issue":"2","first_page":"150","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9269698858261108},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.8242347240447998},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.8061832189559937},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6816338300704956},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5281417369842529},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4938512444496155},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.4520357847213745},{"id":"https://openalex.org/keywords/radical-of-an-integer","display_name":"Radical of an integer","score":0.4249190092086792},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2239130735397339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9269698858261108},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.8242347240447998},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8061832189559937},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6816338300704956},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5281417369842529},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4938512444496155},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.4520357847213745},{"id":"https://openalex.org/C203432157","wikidata":"https://www.wikidata.org/wiki/Q2498974","display_name":"Radical of an integer","level":4,"score":0.4249190092086792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2239130735397339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10998-016-0173-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-016-0173-9","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W10186307","https://openalex.org/W849934788","https://openalex.org/W1577312110","https://openalex.org/W1606063062","https://openalex.org/W1969096882","https://openalex.org/W1998239757","https://openalex.org/W2018835354","https://openalex.org/W2022421308","https://openalex.org/W2027318634","https://openalex.org/W2041544945","https://openalex.org/W2057101465","https://openalex.org/W2080936890","https://openalex.org/W2284242454","https://openalex.org/W2326491596","https://openalex.org/W2954945477","https://openalex.org/W4256355402"],"related_works":["https://openalex.org/W2365502274","https://openalex.org/W2332490159","https://openalex.org/W2348718661","https://openalex.org/W2350917914","https://openalex.org/W2386565732","https://openalex.org/W2371888463","https://openalex.org/W2370263844","https://openalex.org/W2054586790","https://openalex.org/W2383522337","https://openalex.org/W250723459"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-11-30T00:00:00"}