COMP 2711 Ex 14

1

$$\begin{array}{rl}\gcd (57,81)& =x\cdot 57+y\cdot 81\\ & =jx+ky\end{array}$$ $$k=jq+r$$ $$\begin{array}{cccccc}k& j& r& q& x& y\\ 81& 57& 24& 1& 10& -7\\ 57& 24& 9& 2& -7& 3\\ 24& 9& 6& 2& 3& -1\\ 9& 6& 3& 1& -1& 1\\ 6& 3& 0& 2& 1& 0\end{array}$$ $$\begin{array}{rl}& x=10\\ & y=-7\end{array}$$