Publication Information

{'id': 'https://openalex.org/W2371987948', 'doi': None, 'title': 'The Integer Solutions of the Diophantine Equation x~3+1=13qy~2', 'display_name': 'The Integer Solutions of the Diophantine Equation x~3+1=13qy~2', 'publication_year': 2014, 'publication_date': '2014-01-01', 'ids': {'openalex': 'https://openalex.org/W2371987948', 'mag': '2371987948'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://en.cnki.com.cn/Article_en/CJFDTotal-CQSF201406014.htm', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S2764346719', 'display_name': 'Chongqing Shifan Daxue xuebao. Ziran kexue ban', 'issn_l': '1672-6693', 'issn': ['1672-6693'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4366724589', 'host_organization_name': 'Chongqing Normal University', 'host_organization_lineage': ['https://openalex.org/P4366724589'], 'host_organization_lineage_names': ['Chongqing Normal University'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5043102980', 'display_name': 'DU Xian-cu', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I82760581', 'display_name': 'Taizhou University', 'ror': 'https://ror.org/04fzhyx73', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I82760581']}], 'countries': ['CN'], 'is_corresponding': True, 'raw_author_name': 'DU Xiancu', 'raw_affiliation_strings': ['Information Science,Taizhou University'], 'affiliations': [{'raw_affiliation_string': 'Information Science,Taizhou University', 'institution_ids': ['https://openalex.org/I82760581']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5043102980'], 'corresponding_institution_ids': ['https://openalex.org/I82760581'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 66}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9738, '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': 0.9738, '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/T12516', 'display_name': 'Advanced Mathematical Theories and Applications', 'score': 0.9621, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10588', 'display_name': 'Mathematical Dynamics and Fractals', 'score': 0.9568, '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/congruence', 'display_name': 'Congruence (geometry)', 'score': 0.75929534}, {'id': 'https://openalex.org/keywords/quadratic-residue', 'display_name': 'Quadratic residue', 'score': 0.5989451}], 'concepts': [{'id': 'https://openalex.org/C206530611', 'wikidata': 'https://www.wikidata.org/wiki/Q905896', 'display_name': 'Diophantine equation', 'level': 2, 'score': 0.9633931}, {'id': 'https://openalex.org/C97137487', 'wikidata': 'https://www.wikidata.org/wiki/Q729138', 'display_name': 'Integer (computer science)', 'level': 2, 'score': 0.7846997}, {'id': 'https://openalex.org/C132074034', 'wikidata': 'https://www.wikidata.org/wiki/Q154210', 'display_name': 'Congruence (geometry)', 'level': 2, 'score': 0.75929534}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.73599887}, {'id': 'https://openalex.org/C40621787', 'wikidata': 'https://www.wikidata.org/wiki/Q16251580', 'display_name': 'Diophantine set', 'level': 3, 'score': 0.71455157}, {'id': 'https://openalex.org/C12817185', 'wikidata': 'https://www.wikidata.org/wiki/Q878259', 'display_name': 'Quadratic residue', 'level': 2, 'score': 0.5989451}, {'id': 'https://openalex.org/C86287605', 'wikidata': 'https://www.wikidata.org/wiki/Q4454970', 'display_name': "Legendre's equation", 'level': 3, 'score': 0.5928798}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.48039773}, {'id': 'https://openalex.org/C184992742', 'wikidata': 'https://www.wikidata.org/wiki/Q7243229', 'display_name': 'Prime (order theory)', 'level': 2, 'score': 0.47936895}, {'id': 'https://openalex.org/C129844170', 'wikidata': 'https://www.wikidata.org/wiki/Q41299', 'display_name': 'Quadratic equation', 'level': 2, 'score': 0.45225126}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.43174213}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.046845466}, {'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': [{'is_oa': False, 'landing_page_url': 'http://en.cnki.com.cn/Article_en/CJFDTotal-CQSF201406014.htm', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S2764346719', 'display_name': 'Chongqing Shifan Daxue xuebao. Ziran kexue ban', 'issn_l': '1672-6693', 'issn': ['1672-6693'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4366724589', 'host_organization_name': 'Chongqing Normal University', 'host_organization_lineage': ['https://openalex.org/P4366724589'], 'host_organization_lineage_names': ['Chongqing Normal University'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W3150453880', 'https://openalex.org/W3133994288', 'https://openalex.org/W3127045536', 'https://openalex.org/W3092805457', 'https://openalex.org/W3024389873', 'https://openalex.org/W2978626527', 'https://openalex.org/W2978511607', 'https://openalex.org/W2953024552', 'https://openalex.org/W2889318194', 'https://openalex.org/W2373948602', 'https://openalex.org/W2360316567', 'https://openalex.org/W2333524743', 'https://openalex.org/W2313289481', 'https://openalex.org/W2150566934', 'https://openalex.org/W2133417064', 'https://openalex.org/W207958708', 'https://openalex.org/W2061114622', 'https://openalex.org/W2046199877', 'https://openalex.org/W1975709759', 'https://openalex.org/W1621047391'], 'abstract_inverted_index': {'Let': [0], 'D': [1, 8], 'be': [2], 'a': [3], 'square-free': [4], 'positive': [5], 'integer': [6, 68, 86], 'and': [7], '=': [9, 11, 30, 65, 81], '∏si': [10], '1pi(': [12], 's≥2),where': [13], 'pi≡1(': [14], 'mod': [15, 48], '6)(': [16], 'i=': [17], '1,2,…,s)': [18], 'are': [19], 'odd': [20, 52], 'primes.': [21], 'The': [22], 'primary': [23], 'solution': [24], 'of': [25, 40], 'the': [26, 41, 55], 'Diophantine': [27, 62, 78], 'equation': [28, 63, 79], 'x3+1': [29, 64, 80], 'Dy2': [31], 'still': [32], 'remains': [33], 'unresolved.': [34], 'By': [35], 'using': [36], 'congruence,quadratic': [37], 'residue,some': [38], 'properties': [39], 'solutions': [42], 'to': [43], 'Pell': [44], 'equation,recursive': [45], 'sequence,when': [46], 'q≡7(': [47], '12)': [49], 'is': [50], 'an': [51], 'prime,and(q/13)=-1,we': [53], 'prove': [54], 'following': [56], 'results:': [57], '1)': [58], 'if': [59, 76], 'q=': [60], '7,the': [61], '13qy2': [66, 82], 'has': [67, 83], 'solutions(': [69], 'x,y)': [70, 89], '=(': [71], '4': [72], '367,±30': [73], '252),(-1,0);': [74], '2)': [75], 'q≠7,the': [77], 'only': [84], 'one': [85], 'solution,that': [87], 'is(': [88], '=(-1,0).': [90]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2371987948', 'counts_by_year': [], 'updated_date': '2024-12-08T00:39:24.568520', 'created_date': '2016-06-24'}