\input amstex
\def\akko{\;\Longleftrightarrow\;}
\def\pomod#1{\equiv\limits_{#1}}
$$\aligned
50\,a^{-1}\pomod{137}1&\akko 50\,a^{-1}=137\,k+1=100\,k+37\,k+1\akko\cr
\akko 37\,k+1\pomod{50}0&\akko 37\,k+1=50\,\mu=37\,\mu+13\,\mu\akko\cr
\akko 13\,\mu-1\pomod{37}0&\akko 13\,\mu-1=37\,\nu=26\,\nu+11\,\nu\akko\cr
\akko 11\,\nu+1\pomod{13}0&\akko 11\,\nu+1=13\,\rho=11\,\rho+2\,\rho\akko\cr
\akko 2\,\rho-1\pomod{11}0&\akko 2\,\rho-1=11\,\tau=10\,\tau+\tau\akko\cr
\akko \tau+1\pomod{2}0&\akko \tau=2\,\theta-1\akko 2\,\rho-1=22\,\theta-11\akko\cr
\akko \rho=11\,\theta-5&\akko 11\,\nu+1=11\cdot13\,\theta-65\akko\nu=13\,\theta-6\akko\cr
\akko 13\,\mu-1=37\cdot13\theta-222&\akko\mu=37\,\theta-17\akko 37\,k+1=50\cdot37\,\theta-850\akko\cr
\akko k=50\,\theta-23&\akko 50\,a^{-1}-1=137\cdot50\,\theta-3151\akko\fbox{$a^{-1}=137\,\theta-63$}
\endaligned$$