음이 아닌 모든 정수 n n n ( x n , y n ) ( \mathit{x} _{n} , y _{n} ) ( x n , y n )
(가) x 0 = 1 x _{0} = 1 x 0 = 1 y 0 = 0 y _{0} = 0 y 0 = 0
x n + 1 y n + 1 \displaystyle \begin{matrix} x _{n + 1} \\ y _{n + 1} \end{matrix} x n + 1 y n + 1 cos π 8 sin π 8 − sin π 8 cos π 8 \displaystyle \begin{matrix} \cos \frac{\pi}{8} \\ \sin \frac{\pi}{8} \end{matrix} \begin{matrix} - \sin \frac{\pi}{8} \\ \cos \frac{\pi}{8} \end{matrix} cos 8 π sin 8 π − sin 8 π cos 8 π 1 2 0 0 1 2 \displaystyle {\begin{matrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{matrix}} 2 1 0 0 2 1 x n y n \displaystyle \begin{matrix} x _{n} \\ y _{n} \end{matrix} x n y n
x 98 + y 102 = k ( 1 2 ) 103 \displaystyle x _{98} + y _{102} = k \left( \frac{1}{2} \right) ^{103} x 98 + y 102 = k ( 2 1 ) 103 k k k ① 15 2 \displaystyle 15 \sqrt{2} 15 2 ② 17 2 \displaystyle 17 \sqrt{2} 17 2 ③ 19 2 \displaystyle 19 \sqrt{2} 19 2 ④ 21 2 \displaystyle 21 \sqrt{2} 21 2 ⑤ 23 2 \displaystyle 23 \sqrt{2} 23 2
(나)