) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 设g(x)=a0(0(x)+…+cmn9mn(x)则 g(x)=f(x1)=a00(x1)+…+ann(x) (x0)+a191(x)+…+an9n(x0)=f(x0 0(x1)+a192(x1)+…+ann(x)=f(x1) aoPo(n)+a,9(n)+.+amPm(n)=f( 所以{1}=有唯一解,当且仅当m=n,且系数行列 式不为0数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 0 0 0 0 ( ) ( ) ( ) ( ) ( ) ( ) ( ) m m i i i m m i g x a x a x g x f x a x a x     = + + = = + + 设 则 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) m m m m n n m m n n a x a x a x f x a x a x a x f x a x a x a x f x           + + + =   + + + =     + + + = 所以 有唯一解，当且仅当m=n，且系数行列 式不为0 0 { }n i i a =