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1994年第20届全俄中学生数学奥林匹克最后阶段竞赛九年级第一天的第1题(不妨称作题1),原题如下:题1:若(x~2+1~(1/2)+x)(y~2+1~(1/2)+y)=1,证明:x+y=0.笔者一直对题1感兴趣,但因信息闭塞,孤陋寡闻,感觉公开发表的文章中较少涉及题1.就笔者愚见,本题最早进入我国是1995年,详见文[1].(注:不少人将题1称作西班牙数学奥林匹克试题,笔者无从考证,不过这丝毫不影响我们对题1的研究)笔者后来又有幸拜读文[2]、[3]、[4]、[5]、[6]等,近日拜读文[7],再次勾起笔者对此题的欣赏.
The first question (may be called title 1) of the 20th day of the ninth grade of the 20th Olympics National Mathematical Olympiad for the All-Russia Students in the 20th National Congress of the Republic of China in 1994 was as follows: Question 1: If (x ~ 2 + 1 ~ (1/2) + x) (y ~ 2 + 1 ~ (1/2) + y) = 1, prove that: x + y = 0. The author has been interested in the first question, but due to information blockage, ignorant, feel openly published articles Less involved in the title 1. I humble opinion on the author, the earliest entry into our country in 1995, see article [1]. (Note: Many people will title 1 is the Spanish Mathematical Olympiad exam, I have no way of research, but this is not the slightest Affect our research on the title 1) I was fortunate enough to read the text [2], [3], [4], [5], [6], recently read the article [7] enjoy.