关于二次域理论求解一类Diophantus方程的整数解
SOLVING THE INTEGER SOLUTIONS OF A CLASS OF DIOPHANTINE EQUATIONS BY SONE THEORIES ON QUNDRATIC FIELDS

本文研究了两个典型Diophantus方程在实二次域中整数解的问题.利用二次域中的理论和二次代数整数环中算术基本定理,得到了该类方程的一般解法和在实二次域中的所有整数解的相关结论,推广了文献[1]和[2]的结果.
In this paper, we study the integer solutions of two typical Diophantine equations on real quadratic fields. By using some theories on quadratic fields and the fundamental theorem of arithmetic on the ring of quadratic algebraic integers, we obtain the general solving method of this class of Diophantine equations and all the integer solutions, which extend some results in reference [1] and [2]