{"id":"https://openalex.org/W7166327970","doi":"https://doi.org/10.17654/0972087126143","title":"ON THE DIOPHANTINE EQUATION $p^x+(p-2)^y=z^2$","display_name":"ON THE DIOPHANTINE EQUATION $p^x+(p-2)^y=z^2$","publication_year":2026,"publication_date":"2026-06-27","ids":{"openalex":"https://openalex.org/W7166327970","doi":"https://doi.org/10.17654/0972087126143"},"language":"en","primary_location":{"id":"doi:10.17654/0972087126143","doi":"https://doi.org/10.17654/0972087126143","is_oa":true,"landing_page_url":"https://doi.org/10.17654/0972087126143","pdf_url":null,"source":{"id":"https://openalex.org/S2764809114","display_name":"Far East Journal of Mathematical Sciences (FJMS)","issn_l":"0972-0871","issn":["0972-0871","2584-1246"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific"],"host_organization":"https://openalex.org/P4362561667","host_organization_name":"Pushpa Publishing House","host_organization_lineage":["https://openalex.org/P4362561667"],"host_organization_lineage_names":["Pushpa Publishing House"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Far East Journal of Mathematical Sciences (FJMS)","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.17654/0972087126143","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066540994","display_name":"Suton Tadee","orcid":"https://orcid.org/0000-0002-2117-2544","observed_orcids":["https://orcid.org/0000-0002-2117-2544"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Suton Tadee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5066540994"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.42534247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"143","issue":"8","first_page":"2517","last_page":"2524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9965999722480774,"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":0.9965999722480774,"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":0.0020000000949949026,"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":0.9070000052452087},{"id":"https://openalex.org/keywords/exponential-diophantine-equations","display_name":"exponential Diophantine equations","score":0.8569999933242798},{"id":"https://openalex.org/keywords/prime-powers","display_name":"prime powers","score":0.6710000038146973},{"id":"https://openalex.org/keywords/perfect-squares","display_name":"perfect squares","score":0.6949999928474426},{"id":"https://openalex.org/keywords/non-negative-integer-solutions","display_name":"non-negative integer solutions","score":0.9580000042915344},{"id":"https://openalex.org/keywords/congruence-conditions-on-primes","display_name":"congruence conditions on primes","score":0.7620000243186951},{"id":"https://openalex.org/keywords/nonexistence-of-solutions","display_name":"nonexistence of solutions","score":0.7749999761581421}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8741000294685364},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.8312000036239624},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.7621999979019165},{"id":"https://openalex.org/C155635571","wikidata":"https://www.wikidata.org/wiki/Q2378270","display_name":"Thue equation","level":4,"score":0.7378000020980835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7156000137329102},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6550999879837036},{"id":"https://openalex.org/C555856410","wikidata":"https://www.wikidata.org/wiki/Q65122107","display_name":"Diophantine geometry","level":4,"score":0.4779999852180481},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33739998936653137},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3158999979496002},{"id":"https://openalex.org/C98059654","wikidata":"https://www.wikidata.org/wiki/Q5171072","display_name":"Cornacchia's algorithm","level":4,"score":0.3021000027656555},{"id":"https://openalex.org/C203432157","wikidata":"https://www.wikidata.org/wiki/Q2498974","display_name":"Radical of an integer","level":4,"score":0.2994999885559082},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.29159998893737793},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C55247095","wikidata":"https://www.wikidata.org/wiki/Q6889716","display_name":"Modular equation","level":4,"score":0.26269999146461487},{"id":"https://openalex.org/C2779851814","wikidata":"https://www.wikidata.org/wiki/Q5358916","display_name":"Elementary theory","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.17654/0972087126143","doi":"https://doi.org/10.17654/0972087126143","is_oa":true,"landing_page_url":"https://doi.org/10.17654/0972087126143","pdf_url":null,"source":{"id":"https://openalex.org/S2764809114","display_name":"Far East Journal of Mathematical Sciences (FJMS)","issn_l":"0972-0871","issn":["0972-0871","2584-1246"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific"],"host_organization":"https://openalex.org/P4362561667","host_organization_name":"Pushpa Publishing House","host_organization_lineage":["https://openalex.org/P4362561667"],"host_organization_lineage_names":["Pushpa Publishing House"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Far East Journal of Mathematical Sciences (FJMS)","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.17654/0972087126143","doi":"https://doi.org/10.17654/0972087126143","is_oa":true,"landing_page_url":"https://doi.org/10.17654/0972087126143","pdf_url":null,"source":{"id":"https://openalex.org/S2764809114","display_name":"Far East Journal of Mathematical Sciences (FJMS)","issn_l":"0972-0871","issn":["0972-0871","2584-1246"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific"],"host_organization":"https://openalex.org/P4362561667","host_organization_name":"Pushpa Publishing House","host_organization_lineage":["https://openalex.org/P4362561667"],"host_organization_lineage_names":["Pushpa Publishing House"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Far East Journal of Mathematical Sciences (FJMS)","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7155561335","https://openalex.org/W4401466842","https://openalex.org/W4417212870","https://openalex.org/W2421041352","https://openalex.org/W2156359233","https://openalex.org/W4307765621","https://openalex.org/W2810344868","https://openalex.org/W2058511924","https://openalex.org/W7115906031","https://openalex.org/W1492620247"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,25],"investigate":[4],"non-negative":[5],"integer":[6],"solutions":[7],"$(x,":[8,40],"y,":[9,41],"z)$":[10],"of":[11,36],"the":[12,34,37,66],"Diophantine":[13],"equation":[14,38,67],"$p^x+(p-2)^y=z^2$,":[15],"when":[16],"$p$":[17],"is":[18,39,46],"a":[19,47],"prime":[20],"number.":[21],"Using":[22],"elementary":[23],"methods,":[24],"prove":[26],"that":[27],"if":[28,51],"$p":[29,52,56,61],"\\equiv":[30,53,57,62],"5(\\bmod":[31],"8)$,":[32,55],"then":[33,65],"solution":[35],"z)=(0,1,":[42],"\\sqrt{p-1})$,":[43],"where":[44],"$z=\\sqrt{p-1}$":[45],"positive":[48],"integer.":[49],"Moreover,":[50],"7(\\bmod":[54,63],"11(\\bmod":[58],"12)$":[59],"or":[60],"20)$,":[64],"has":[68],"no":[69],"solution.":[70]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-06-28T00:00:00"}
