{"id":"W2061426624","doi":"10.1017/s0013091508000989","title":"Square-free values of quadratic polynomials","year":2010,"lang":"en","type":"article","venue":"Proceedings of the Edinburgh Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Square (algebra); Mathematics; Quadratic equation; Polynomial; Combinatorics; Relation (database); Quadratic function; Square-free integer; Discrete mathematics; Mathematical analysis; Computer science; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002387737,0.0005222512,0.000901193,0.002720103,0.00113038,0.002552183,0.00142747,0.0008089588,0.006591801],"category_scores_gemma":[0.02725552,0.0004810362,0.0005158989,0.0009775027,0.004509042,0.004169664,0.002355389,0.002143761,0.0005628477],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001303372,"about_ca_system_score_gemma":0.0005590066,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007456913,"about_ca_topic_score_gemma":0.0006318625,"domain_scores_codex":[0.9985059,0.0002850287,0.0000603597,0.000283381,0.0005665461,0.0002987724],"domain_scores_gemma":[0.9842362,0.01061468,0.000954763,0.00108581,0.001704259,0.001404379],"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":[0.0005285966,0.0001021886,0.006247276,0.0004258941,0.0000505358,0.0007967738,0.0007557009,0.007510165,0.01654903,0.9443709,0.002859586,0.01980323],"study_design_scores_gemma":[0.00009981035,0.0002343369,0.006218689,0.0001352575,0.00004469921,0.001630502,0.0004071907,0.06535168,0.0104558,0.9095312,0.00580213,0.00008883804],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9181507,0.001519265,0.0373992,0.001474941,0.0001942654,0.0000240966,0.0001439841,0.0004075219,0.04068594],"genre_scores_gemma":[0.9941175,0.0001687983,0.002245653,0.0001086199,0.0001481475,0.00001648333,0.0000853745,0.00004604884,0.00306329],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006591801,"threshold_uncertainty_score":0.02205175,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03352372696414915,"score_gpt":0.3222971631365863,"score_spread":0.2887734361724371,"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."}}