{"id":"W3206798471","doi":"10.1142/s1793042123500148","title":"The Euler totient function on Lucas sequences","year":2022,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Calgary","keywords":"Euler's totient function; Fibonacci number; Mathematics; Lucas sequence; Combinatorics; Euler's formula; Diophantine equation; Number theory; Fibonacci polynomials; Lucas number; Discrete mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003640249,0.0001144451,0.0001488409,0.0001213348,0.0003363523,0.00009571498,0.001025515,0.00002549028,0.01315135],"category_scores_gemma":[0.001577006,0.00007527086,0.0002142902,0.0001315646,0.0001442202,0.0001361791,0.0002261984,0.0005996325,0.0001340747],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004997315,"about_ca_system_score_gemma":0.0001844152,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003509574,"about_ca_topic_score_gemma":0.000002229279,"domain_scores_codex":[0.9967506,0.0007259514,0.000491657,0.000122338,0.001711356,0.0001980926],"domain_scores_gemma":[0.9945729,0.004062026,0.0004682816,0.0002100703,0.0006113239,0.00007542069],"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":[0.001578539,0.00024206,0.0004715646,0.000003130691,0.0005934331,0.0001376233,0.0004928001,0.000203094,0.0000472471,0.9200196,0.06381136,0.01239957],"study_design_scores_gemma":[0.0003886975,0.0001619572,0.0001755573,0.00002357271,0.00003158101,0.0006173163,0.002211075,0.00006565408,0.00007990482,0.8760501,0.1201136,0.00008092749],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7320207,0.0003807159,0.01530251,0.02022692,0.02037802,0.000611703,0.0002485768,0.0001110983,0.2107198],"genre_scores_gemma":[0.9883025,0.00001945401,0.0001730489,0.0004580225,0.0006490355,0.00001833089,0.000004149022,0.00002427293,0.01035114],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2562819,"threshold_uncertainty_score":0.9877508,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04968691522507526,"score_gpt":0.366405080860995,"score_spread":0.3167181656359197,"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."}}