据笔者所知 ,文 [1 ]首先提出并“证明”了一个数学奥林匹克问题 :已知 a,b,c为非负实数 ,且 ab+ bc+ ca= 1 .求证 :1a+ b+ 1b+ c+ 1a+ c≥ 52 . ( * )为便于分析 ,我们将文 [1 ]的“证明”(部分 )抄录如下 :由对称性 ,可设 a≥ b≥c≥ 0 .由所给条件易知 a≥b0 .1b+ c + 1a+ According to the author’s knowledge, [1] first proposed and “proved” a mathematical Olympics problem: a, b, c are known as non-negative real numbers, and ab+ bc + ca = 1. Proof: 1a+ b+ 1b+ c+ 1a+ c≥ 52 (*) For ease of analysis, we will transcribe the “proof” (part) of [1] as follows: From symmetry, we can set a ≥ b ≥ c ≥ 0. Known by the given condition a ≥ b0 .1b + c + 1a+