ユークリッドの互除法
r 2 = k 2 r 3 + r 4 ( 0 < r 4 < r 3 ) {\displaystyle r_{2}=k_{2}r_{3}+r_{4}\ \ (0<r_{4}<r_{3})}
. . . {\displaystyle ...}
r h − 1 = k h − 1 r h + 0 {\displaystyle r_{h-1}=k_{h-1}r_{h}+0}
が得られるとき、
( r 0 r 1 ) = ( k 0 1 1 0 ) ( r 1 r 2 ) {\displaystyle {\begin{pmatrix}r_{0}\\r_{1}\\\end{pmatrix}}={\begin{pmatrix}k_{0}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}r_{1}\\r_{2}\\\end{pmatrix}}}
( r 1 r 2 ) = ( k 1 1 1 0 ) ( r 2 r 3 ) {\displaystyle {\begin{pmatrix}r_{1}\\r_{2}\\\end{pmatrix}}={\begin{pmatrix}k_{1}&1\\1&0\\\end{pmatrix}}{\begin{pmatrix}r_{2}\\r_{3}\\\end{pmatrix}}}