{"id":"W1977507299","doi":"10.4153/cmb-2002-045-2","title":"Criteria for Simultaneous Solutions of <i>X</i><sup>2</sup> − <i>DY</i><sup>2</sup> = <i>c</i> and <i>x</i><sup>2</sup> − <i>Dy</i><sup>2</sup> = −<i>c</i>","year":2002,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Diophantine equation; Pure mathematics; Square (algebra); Discrete mathematics; Algebra over a field; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003730678,0.001538023,0.001558422,0.003451837,0.00273112,0.003212373,0.001959776,0.003159216,0.0129742],"category_scores_gemma":[0.02789145,0.0009411909,0.001501166,0.00109664,0.004127979,0.00458818,0.005768328,0.003317641,0.001390703],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001031667,"about_ca_system_score_gemma":0.001479376,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007609381,"about_ca_topic_score_gemma":0.0009356322,"domain_scores_codex":[0.9968114,0.0006133605,0.0004522361,0.0005466591,0.001081561,0.0004947336],"domain_scores_gemma":[0.9750878,0.01446441,0.002943242,0.0006199337,0.004576954,0.002307714],"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":[0.001273835,0.000253314,0.00771565,0.0008752935,0.0001855836,0.004143696,0.003775322,0.01967562,0.04259667,0.884269,0.0051796,0.03005642],"study_design_scores_gemma":[0.0006693965,0.001420583,0.00390981,0.000354194,0.0001930462,0.003067302,0.003884156,0.1521384,0.04011948,0.776169,0.01777329,0.0003013577],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5915586,0.001628403,0.3241742,0.0038373,0.000508032,0.0008163106,0.0006839919,0.0005668558,0.07622622],"genre_scores_gemma":[0.9356588,0.0003397904,0.05332787,0.0002065108,0.0002525871,0.0005439054,0.0004646672,0.0001312989,0.009074455],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0129742,"threshold_uncertainty_score":0.04340303,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03571964801635275,"score_gpt":0.2664953362472899,"score_spread":0.2307756882309371,"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."}}