{"id":"W4200230425","doi":"10.24193/mathcluj.2021.2.01","title":"A note on the Diophantine Equation x^2-kxy+ky^2+ly=0","year":2021,"lang":"en","type":"article","venue":"Mathematica","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Diophantine equation; Mathematics; Legendre's equation; Characterization (materials science); Diophantine set; Pure mathematics; Discrete mathematics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"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":[0.0004284161,0.0008450538,0.0005496523,0.0006727018,0.001414535,0.001195764,0.000812722,0.0009054681,0.006547368],"category_scores_gemma":[0.0007830656,0.0002736718,0.0005518766,0.0007784008,0.001364052,0.001438485,0.00097995,0.002762972,0.001934401],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007577575,"about_ca_system_score_gemma":0.0005002744,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001669105,"about_ca_topic_score_gemma":0.002358017,"domain_scores_codex":[0.9998851,0.00002244635,0.000008101403,0.00001965723,0.00004388939,0.00002079965],"domain_scores_gemma":[0.9998062,0.00009892423,0.00002472132,0.00001546183,0.00002675764,0.00002797368],"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":[0.000135249,0.00006835515,0.0007938351,0.0005477726,0.00003381025,0.00197431,0.0006733129,0.004551054,0.0170732,0.8955611,0.0450456,0.03354244],"study_design_scores_gemma":[0.00004371744,0.0001906655,0.001957432,0.0001333195,0.00004319106,0.001097744,0.0002633172,0.00828536,0.00399853,0.7977626,0.1861653,0.00005878977],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2083148,0.0404609,0.1026014,0.0510594,0.03463823,0.0001106398,0.0006673029,0.0005626082,0.5615847],"genre_scores_gemma":[0.700359,0.02407708,0.04024522,0.008943262,0.01132101,0.00008047999,0.0004348339,0.0003866482,0.2141525],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006547368,"threshold_uncertainty_score":0.0219031,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02384575385760119,"score_gpt":0.2873008945309518,"score_spread":0.2634551406733506,"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."}}