{"id":"W2312652594","doi":"10.1112/s0025579316000231","title":"PERFECT POWERS THAT ARE SUMS OF CONSECUTIVE CUBES","year":2016,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Perfect power; Logarithm; Euler's formula; Sums of powers; Relation (database)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009718871,0.0005010563,0.0009262533,0.001182751,0.001810621,0.002183401,0.0006205988,0.0007578929,0.007491688],"category_scores_gemma":[0.01112966,0.0006431499,0.001005108,0.001672511,0.003417893,0.007548259,0.002196323,0.001550793,0.0009881435],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007115019,"about_ca_system_score_gemma":0.0005055958,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006965714,"about_ca_topic_score_gemma":0.0008773843,"domain_scores_codex":[0.9983636,0.0002670618,0.0001818835,0.0004735532,0.0003842848,0.0003296961],"domain_scores_gemma":[0.9958015,0.002193077,0.0005637522,0.0006533406,0.0005208508,0.0002674445],"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":[0.0003349862,0.00004750421,0.007102724,0.0002465466,0.0000664066,0.002073454,0.000921426,0.004907849,0.006152361,0.9272216,0.006087624,0.04483743],"study_design_scores_gemma":[0.000042694,0.00007011835,0.002392646,0.00006848151,0.00005063312,0.002393145,0.0005976922,0.00616441,0.007804611,0.9554184,0.0249279,0.00006929344],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.795351,0.001279686,0.1067006,0.001636757,0.0004651727,0.000149932,0.0009996119,0.0003047133,0.09311252],"genre_scores_gemma":[0.9559453,0.0003886467,0.03026112,0.0002760084,0.0001639809,0.00004685979,0.0005097416,0.0001007089,0.01230774],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007491688,"threshold_uncertainty_score":0.02506214,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08656458321088152,"score_gpt":0.347010285099643,"score_spread":0.2604457018887615,"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."}}