文档介绍：马尔可夫数: A Markov number is an integer x ,y orz that fits in the Diophantine equation x 2+y 2+z 2 =3 xyz and gives a Lagrange number L x=9?4x 2 (ory orz as the case may be). The solutions , (1, 1, 1), (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), (1, 13, 34), (1, 34, 89), (2, 29, 169), (5, 13, 194), (1, 89, 233), etc., can be put ina binary graph tree . Thus arranged, the numbers on 1's branch are i numbers with odd index , and the numbers on 2's branch are Pell numbers with odd index. Frobenius proved that, with the exception of the smallest Markov triple, the numbers in a Markov triple are pairwise coprime . He also proved that an odd Markov number x 1mod4 (ory orz ) and an even Markov number x 2mod8 . Ying Zhang used this to prove that even Markov numbers satisfy the sharper congruence x 2mod32 , which he calls the best possible since the first two even Markov numbers are 2 and 34. 上述资料参考网站: /encyclopedia/ http://en./wiki/Markov_number 下属资料参考网站: i/%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E6%96%B9%E7%A8% 8B?prd=fenleishequ_jiaodiantuijian_zuotu 不定方程称为马尔可夫方程。求解方法如下: 先凭观察找出(x1,x2,x3) = (1,1,1) 这组解。方程可视为一个 x3 为未知数的一元二次方程。根据韦达定理,可知(x1,x2,3x1x2 ? x3) (留意)也是一个解。这个方程有无限个解。事实上,用这个方法由(1,1,1) 开始,可以找出这方程的所有正整数数组解。在此不定方程的解出现的正整数称为马尔可夫数( Markov number ),它们由小到大是: 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... ( OEIS:A002559 ) 它们组成的解是: (1, 1, 1), (1, 1, 2), (1,