Analogously to 13B, find an algorithm which, for relatively prime numbers $a_0$ and $a_1$, produces numbers $p_0$ and $p_1$ with $p_0 a_0+p_1 a_1=1$. Conclude that for each number $n\left(=a_1\right)$, every element of $Z_n$ relatively prime with $n$ has an inverse element which can be found by the Euclidean algorithm.