十九世纪的俄国杰出数学家马尔柯夫(1856—1922)曾提出一个著名的不定方程: x~2+y~2+z~2=3xyz (1) 并且仅仅使用了初等数学方法(包括韦达定理)就求得了方程的全部解,所以本文所介绍的内容是一般中学生也能接受的。 在把x=a,y=b,z=c代入原方程后而恒等时,我们就把数组(a,b,c)称为是这个不定方程的解,而把a,b,c这三个数称为解的坐标。我 The outstanding Russian mathematician Markov (1856–1922) of the 19th century proposed a well-known indefinite equation: x~2+y~2+z~2=3xyz (1) and used only elementary mathematics (including Wei Theorem) has obtained all the solutions of the equation, so the content introduced in this article is acceptable to the average middle school student. After substituting x=a, y=b, and z=c into the original equation and then identity, we call the array (a,b,c) the solution of this indefinite equation, and put a,b,c The three numbers are called the coordinates of the solution. I