{"id":"https://openalex.org/W3127045536","doi":"https://doi.org/10.37394/23206.2020.19.56","title":"On the Diophantine Equation 8^x+n^y=z^2","display_name":"On the Diophantine Equation 8^x+n^y=z^2","publication_year":2020,"publication_date":"2020-10-30","ids":{"openalex":"https://openalex.org/W3127045536","doi":"https://doi.org/10.37394/23206.2020.19.56","mag":"3127045536"},"language":"en","primary_location":{"id":"doi:10.37394/23206.2020.19.56","doi":"https://doi.org/10.37394/23206.2020.19.56","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23206.2020.19.56","pdf_url":"https://doi.org/10.37394/23206.2020.19.56","source":{"id":"https://openalex.org/S4210205242","display_name":"WSEAS TRANSACTIONS ON MATHEMATICS","issn_l":"1109-2769","issn":["1109-2769","2224-2880"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","poland-20","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS TRANSACTIONS ON MATHEMATICS","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37394/23206.2020.19.56","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073801702","display_name":"Wachirarak Orosram","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210091243","display_name":"Buriram Rajabhat University","ror":"https://ror.org/00cgkxv41","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210091243"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Wachirarak Orosram","raw_affiliation_strings":["Department of Mathematics, Buriram Rajabhat University, Buriram, THAILAND","Chalermwut Comemuang Department of Mathematics Buriram Rajabhat University 31000, Buriram THAILAND","Department of Mathematics Buriram Rajabhat University 31000, Buriram THAILAND"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Buriram Rajabhat University, Buriram, THAILAND","institution_ids":["https://openalex.org/I4210091243"]},{"raw_affiliation_string":"Chalermwut Comemuang Department of Mathematics Buriram Rajabhat University 31000, Buriram THAILAND","institution_ids":["https://openalex.org/I4210091243"]},{"raw_affiliation_string":"Department of Mathematics Buriram Rajabhat University 31000, Buriram THAILAND","institution_ids":["https://openalex.org/I4210091243"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020612113","display_name":"Chalermwut Comemuang","orcid":"https://orcid.org/0000-0002-7817-1729","observed_orcids":["https://orcid.org/0000-0002-7817-1729"]},"institutions":[{"id":"https://openalex.org/I4210091243","display_name":"Buriram Rajabhat University","ror":"https://ror.org/00cgkxv41","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210091243"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Chalermwut Comemuang","raw_affiliation_strings":["Department of Mathematics, Buriram Rajabhat University, Buriram, THAILAND"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Buriram Rajabhat University, Buriram, THAILAND","institution_ids":["https://openalex.org/I4210091243"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210091243"],"apc_list":null,"apc_paid":null,"fwci":0.6799,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57832771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":95},"biblio":{"volume":"19","issue":null,"first_page":"520","last_page":"522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9984999895095825,"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":0.9984999895095825,"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":0.0003000000142492354,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diophantine-equations","display_name":"Diophantine equations","score":0.9160000085830688},{"id":"https://openalex.org/keywords/exponential-diophantine-equations","display_name":"exponential Diophantine equations","score":0.9520000219345093},{"id":"https://openalex.org/keywords/perfect-squares","display_name":"perfect squares","score":0.5460000038146973},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.7239999771118164}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.9602279663085938},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8753844499588013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5900986194610596},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.487018883228302},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4600055515766144},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4012201130390167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0870867371559143},{"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:10.37394/23206.2020.19.56","doi":"https://doi.org/10.37394/23206.2020.19.56","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23206.2020.19.56","pdf_url":"https://doi.org/10.37394/23206.2020.19.56","source":{"id":"https://openalex.org/S4210205242","display_name":"WSEAS TRANSACTIONS ON MATHEMATICS","issn_l":"1109-2769","issn":["1109-2769","2224-2880"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","poland-20","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS TRANSACTIONS ON MATHEMATICS","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37394/23206.2020.19.56","doi":"https://doi.org/10.37394/23206.2020.19.56","is_oa":true,"landing_page_url":"https://doi.org/10.37394/23206.2020.19.56","pdf_url":"https://doi.org/10.37394/23206.2020.19.56","source":{"id":"https://openalex.org/S4210205242","display_name":"WSEAS TRANSACTIONS ON MATHEMATICS","issn_l":"1109-2769","issn":["1109-2769","2224-2880"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","poland-20","russia-white-list-3","vabb-shw"],"host_organization":"https://openalex.org/P4310320666","host_organization_name":"World Scientific and Engineering Academy and Society","host_organization_lineage":["https://openalex.org/P4310320666"],"host_organization_lineage_names":["World Scientific and Engineering Academy and Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"WSEAS TRANSACTIONS ON MATHEMATICS","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3127045536.pdf","grobid_xml":"https://content.openalex.org/works/W3127045536.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1492620247","https://openalex.org/W2041544945","https://openalex.org/W2073551927","https://openalex.org/W2727786984","https://openalex.org/W3041625430","https://openalex.org/W3130988621","https://openalex.org/W4234298921","https://openalex.org/W4252738515","https://openalex.org/W4253754805"],"related_works":["https://openalex.org/W4321614863","https://openalex.org/W4234298921","https://openalex.org/W4416915487","https://openalex.org/W4233653727","https://openalex.org/W2073551927","https://openalex.org/W3208118492","https://openalex.org/W2034227168","https://openalex.org/W7127952567","https://openalex.org/W7219194160","https://openalex.org/W3211415143"],"abstract_inverted_index":{"Let":[0],"n":[1,7],"be":[2],"an":[3],"positive":[4],"integer":[5,21],"with":[6],"=":[8],"10(mod15).":[9],"In":[10],"this":[11],"paper,":[12],"we":[13],"prove":[14],"that":[15],"(1,0,3)":[16],"is":[17],"unique":[18],"non":[19],"negative":[20],"solution":[22],"(x,y,z)":[23],"of":[24],"the":[25],"Diophantine":[26],"equation":[27],"8^x+n^y=z^2":[28],"where":[29],"x":[30],"y,":[31],"and":[32],"z":[33],"are":[34],"non-negativeintegers.":[35]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2021-02-15T00:00:00"}