3(x+y)^2=7(x^3+y^3)>=0,x+y>=0....1)3(x+y)^2=7(x^3+y^3)=7(x+y)[(x+y)^2-3xy]>=7(x+y)[(x+y)^2-3(x+y)^2/4]=7(x+y)^3/4x+y<=12/7...2)1),2):x+y=0或x+y=1(不满足)所以:只要满足x+y=0式子的整数都是整数解例如(1,-1),(-2,2).....,