{"id":"W2962907707","doi":"10.1142/s1793042111004526","title":"COMMON DIVISORS OF VALUES OF POLYNOMIALS AND COMMON FACTORS OF INDICES IN A NUMBER FIELD","year":2011,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Integer (computer science); Discriminant; Combinatorics; Prime factor; Prime (order theory); Degree (music); Field (mathematics); Algebraic number field; Polynomial; Greatest common divisor; Discrete mathematics; Pure mathematics; Mathematical analysis","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":[0.002074627,0.0007579153,0.0009231749,0.002827078,0.001341683,0.003954305,0.001131661,0.0006228336,0.003986179],"category_scores_gemma":[0.008956009,0.0005805273,0.0008576571,0.002242596,0.003586263,0.005919231,0.002163187,0.001675286,0.0006930121],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001837546,"about_ca_system_score_gemma":0.0008414721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004616468,"about_ca_topic_score_gemma":0.0005244869,"domain_scores_codex":[0.9987458,0.0001831828,0.0001173075,0.0003793171,0.0003526605,0.0002217296],"domain_scores_gemma":[0.9956565,0.00241998,0.0007113609,0.0004759033,0.0002649524,0.0004713509],"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":[0.001522681,0.0001824986,0.01433104,0.0003912961,0.00005375487,0.001408845,0.002099191,0.008164708,0.01255061,0.8606471,0.002664967,0.09598318],"study_design_scores_gemma":[0.0001573863,0.0004307274,0.00464366,0.0002076628,0.0001340789,0.00252581,0.001129673,0.03244854,0.01889831,0.9130304,0.02629408,0.00009975872],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8118688,0.0023376,0.1468894,0.0005099495,0.0001630045,0.0001481372,0.0003806337,0.0003699832,0.0373325],"genre_scores_gemma":[0.9417781,0.0008846498,0.05163314,0.00005983006,0.0002271466,0.00007241612,0.0004076796,0.00006946712,0.004867667],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003986179,"threshold_uncertainty_score":0.01333511,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07222795215816397,"score_gpt":0.3820572551630411,"score_spread":0.3098293030048772,"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."}}