一类Diophantine方程在实二次Euclid域上的整数解

Solving the Integer Solutions of a Class of Diophantine Equations on Real Quadratic Euclid Fields

研究了一类典型的Diophantine方程在实二次Euclid域中的整数解问题。主要利用二次域中的理论和二次代数整数环中算术基本定理,证明了此类Diophantine方程在特殊情形下无整数解的相关结论。

We studied the integer solutions of class typical Diophantine equations on real quadratic Euclid fields. By using some theories on quadratic fields and fundamental theorem of arithmetic on the ring of quadratic algebraic integer, we proved that the equations didn＇ t have integer solution.