0534132人目の素数さん
2018/04/24(火) 11:04:06.96ID:43b+grE0〔補題〕
(A^3+B^3+C^3)^2 ≧ (AB+BC+CA)(A^4+B^4+C^4)
(左辺) - (右辺) = F_0(A,B,C) F_0(AA,BB,CC) + (ABC)^2 F_{-2}(A,B,C) ≧ 0,
F_0(A,B,C) = (A-B)(A-C) + (B-C)(B-A) + (C-A)(C-B) = {(A-B)^2 + (B-C)^2 + (C-A)^2}/2 ≧ 0,
F_{-2}(A,B,C) = (A-B)(A-C)/AA + (B-C)(B-A)/BB + (C-A)(C-B)/CC = ABC F_1(1/A,1/B,1/C) ≧ 0,