Markoff方程与幂零矩阵
Markoff Equation and Nilpotent Matrices
摘要：
正整数的三元组（a，b，c）称为马尔可夫三元组当且仅当它满足丢番图方程a2 + b2 + c2 = abc。在积分上三角3 × 3矩阵的框架下，重新构造其顶点为马尔可夫三元组的马尔可夫树，将表明这样的三元组的最大成员唯一地确定其他两个。这回答了一个近100年来一直悬而未决的问题。
英文摘要：
A triple (a,b,c) of positive integers is called a Markoff triple iff it satisfies the diophantine equation a2 + b2 + c2 = abc . Recasting the Markoff tree, whose vertices are Markoff triples, in the framework of intergral upper triangular 3x3 matrices, it will be shown that the largest member of such a triple determines the other two uniquely. This answers a question which has been open for almost 100 years.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
