{"id":"W4302863679","doi":"10.48550/arxiv.1011.2154","title":"Reducing the Erdos-Moser equation 1^n + 2^n + . . . + k^n = (k+1)^n\\n modulo k and k^2","year":2010,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Divisibility rule; Modulo; Congruence (geometry); Diophantine equation; Congruence relation; Quotient; Conjecture; Fermat's Last Theorem; Corollary; Mathematical proof; Combinatorics; Pure mathematics; Diophantine approximation; Discrete mathematics","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":[0.00078766,0.0005504925,0.0004680601,0.0007273486,0.00164807,0.00174121,0.0005789616,0.0006781133,0.006708822],"category_scores_gemma":[0.003554478,0.0002177789,0.0008734521,0.0004624898,0.002638066,0.003622701,0.003091905,0.002566124,0.001099104],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001009465,"about_ca_system_score_gemma":0.0009145879,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007840471,"about_ca_topic_score_gemma":0.001232501,"domain_scores_codex":[0.9993472,0.0001266991,0.00005158749,0.0001629589,0.0001570334,0.0001546208],"domain_scores_gemma":[0.9994592,0.0002181958,0.00007707298,0.00006810079,0.00009482454,0.00008253959],"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":[0.00005786207,0.00003239428,0.0003804288,0.00006454636,0.000008335185,0.0003136974,0.0006305241,0.0007049158,0.002959313,0.9811146,0.002736463,0.01099702],"study_design_scores_gemma":[0.00003857413,0.0000407588,0.0002750898,0.00002301204,0.00001620186,0.0003263431,0.0002960427,0.002539722,0.003695475,0.9783611,0.01437246,0.00001527059],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5284876,0.00105714,0.1042384,0.009253095,0.002084256,0.0001680456,0.0002097599,0.0002727238,0.354229],"genre_scores_gemma":[0.9227118,0.0009440415,0.02941442,0.00130215,0.0008460688,0.00009128554,0.0002259393,0.0001445143,0.04431971],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006708822,"threshold_uncertainty_score":0.02244329,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.132850175330639,"score_gpt":0.2264184052056978,"score_spread":0.09356822987505875,"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."}}