Alternative way of calculating the multiplicative inverse Suppose I want to find the inverse of $7^{-1} \equiv 1 \mod 19 $, is there a quick way to do instead of extended euclidean algorithm? (Assume the numbers are not large).
Thank you

I sometimes look at the two multiples that straddle the modular base.
$\color{blue}{2}\cdot 7 = 14 \equiv \color{green}{-5} \bmod 19 \\
\color{orange}{3} \cdot 7 = 21 \equiv \color{red}{2} \bmod 19 $
And then combine those to get the inverse:
$1\cdot \color{green}{-5}  + 3\cdot \color{red}{2} = 1 \\
\implies (1\cdot \color{blue}{2}+ 3\cdot \color{orange}{3}) \cdot 7  \equiv 1 \bmod 19 \\
\implies  7^{-1}  \equiv 11 \bmod 19$
