{"id":"W2408385882","doi":"","title":"Solutions of Some Diophantine Equations Using Generalized Fibonacci and Lucas Sequences.","year":2013,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Mathematics; Lucas sequence; Diophantine equation; Lucas number; Diophantine set; Fibonacci polynomials; Pisano period; Combinatorics; Discrete mathematics; Pure mathematics; Classical orthogonal polynomials; Orthogonal polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00005882037,0.00008827238,0.0001598864,0.00002497731,0.0001745069,0.00002347731,0.00008139542,0.00002054075,0.0002684126],"category_scores_gemma":[0.00001432367,0.0000804668,0.00004409585,0.0001322864,0.0001070675,0.000207798,0.0000669486,0.00005546876,0.0000165514],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009359595,"about_ca_system_score_gemma":0.00002387149,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001716846,"about_ca_topic_score_gemma":2.193767e-7,"domain_scores_codex":[0.9994098,0.00001689473,0.0002077124,0.0001245631,0.00007463263,0.0001663858],"domain_scores_gemma":[0.9994648,0.0001124096,0.0001003126,0.0001794033,0.00007921072,0.00006382622],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[5.493945e-7,0.00006312786,0.0001966958,0.00000681476,0.00001807587,3.611903e-8,0.00004736314,0.00004887952,0.009108586,0.9899034,0.00004811666,0.0005583885],"study_design_scores_gemma":[0.0002902413,0.00001021232,0.0001196595,0.00001327044,0.0000209886,3.136723e-7,0.0001091005,0.005469304,0.002339733,0.9914336,0.0001041114,0.00008944986],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9636093,0.0001337087,0.03407345,0.0002719359,0.0001287334,0.0003118653,0.00002546071,0.00002408324,0.001421444],"genre_scores_gemma":[0.9933596,0.000004424052,0.006371352,0.00001512953,0.00001803812,0.00006257257,0.00001267414,0.000009683721,0.0001464818],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02975032,"threshold_uncertainty_score":0.3281341,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02505496344464397,"score_gpt":0.2798778123028814,"score_spread":0.2548228488582374,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}