求方程(x+y)/(x^2-xy+y^2)=3/7的整数解
问题描述：
求方程(x+y)/(x^2-xy+y^2)=3/7的整数解
1
答
(x+y)/(x^2-xy+y^2)=3/7设x+y=3tx^2-xy+y^2=7tt为整数于是x^2+2xy+y^2=9t^23xy=9t^2-7t(x-y)^2=(28t-9t^2)/3则t是3的倍数,于是,设t=3k则(x-y)^2=28k-27k^2=k(28-27k)≥0又k是整数,于是k=0或1当k=0时,分母为0,舍弃,于...