求证：任意a,b,ca,b,ca,b,c∈N+N_+N+ 若满足a2+b2=c2a^2+b^2=c^2a2+b2=c2且(a,b)=1(a,b)=1(a,b)=1 则存在x,yx,yx,y使a=x2−y2,b=2xy,c=x2+y2a=x^2-y^2,b=2xy,c=x^2+y^2a=x2−y2,b=2xy,c=x2+y2 或a=2xy,b=x2−y2,c=x2+y2a=2xy,b=x^2-y^2,c=x^2+y^2a=2xy,b=x2−y2,c=x2+y2
