ユークリッドの互除法
( r 2 r 3 ) = ( k 2 1 1 0 ) ( r 3 r 4 ) {\displaystyle {\begin{pmatrix}r_{2}\\r_{3}\\\end{pmatrix}}={\begin{pmatrix}k_{2}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}r_{3}\\r_{4}\\\end{pmatrix}}}
. . . {\displaystyle ...}
( r h − 1 r h ) = ( k h − 1 1 1 0 ) ( r h 0 ) {\displaystyle {\begin{pmatrix}r_{h-1}\\r_{h}\\\end{pmatrix}}={\begin{pmatrix}k_{h-1}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}r_{h}\\0\\\end{pmatrix}}}
すなわち
( r 0 r 1 ) = ( k 0 1 1 0 ) ( k 1 1 1 0 ) ( k 2 1 1 0 ) ( k 3 1 1 0 ) . . . ( k h − 1 1 1 0 ) ( r h 0 ) {\displaystyle {\begin{pmatrix}r_{0}\\r_{1}\\\end{pmatrix}}={\begin{pmatrix}k_{0}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}k_{1}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}k_{2}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}k_{3}&1\\1&0\\\end{pmatrix}}...{\begin{pmatrix}k_{h-1}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}r_{h}\\0\\\end{pmatrix}}}