齐次丢番图方程（x＋gk）~T=（x＋gn）~r

The Homogeneous Diophantine Equation

用初等方法证明了：当ｎ，ｘ，ｒ为正整数目ｒ＞３，ｓ为非负整数，ｇ＝８０ｓ＋６，ｇｃｄ（ｘ，ｇ）＝１，丢番图方程无整数解。

By using elementary method,it is proved that when n,x,r are peitive integers withr>3,s is,nonnegative integer,g=80s+6,gcd (x,g)=1,the equation hasno integral solution.