(1)定理:设x0,x1,x2,...是无穷实数列,xj>0,j>=1,那么,
      (i)对任意的整数 n>= 1, r>=1有
            <X0,...,Xn-1,Xn,...,Xn+r> = <X0,...,Xn-1,<Xn,...,Xn+r>> 
            =   <X0,...,Xn-1,Xn+1/<Xn+1,...,Xn+r>>.
      特别地有
            <X0,...,Xn-1,Xn,Xn+1> = <X0,...,Xn-1,Xn+1/Xn+1>
      注:用该定理可以求连分数的值

(2)对于连分数数数列 <X0,...Xn> 有递推关系:
      Pn = XnPn-1+Pn-2;
      Qn = XnQn-1+Qn-2;
      定义:  P-2 = 0; P-1 = 1; Q-2 = 1; Q-1 = 0;
      所以:  P0 = X0; Q0 = 1; P1 = X1X0+1; Q1 = X1;
      特别地:当 Xi=1 时, {Pn}, {Qn}为Fbi数列

(3)pell方程: x^2+ny^2=+-1的解法:
      若n是平方数,则无解, 否则:
      先求出sqrt(n)的连分数序列<x0,x1..xn> 其中xn = 2*x0;
      对于 x^2+ny^2=-1
      若n为奇数,则 x=Pn-1, y=Qn-1; n为偶数时无解
      对于 x^2+ny^2=1
      若n为偶数,则 x=Pn-1, y=Qn-1; n为奇数时x=P2n-1, y=Q2n-1
      注:以上说的解均为最小正解