Expanding the number $a / b$ into a continued fraction, solve the equations $a x - b y = 1$ in integers, if
a) $a=101, b=13$
b) $a=79, b=19$.
a) ${ }^{101} / 13=[7 ; 1,3,3] .[7 ; 1,3]=31 / 4$, so (see problem $\left.\underline{60603}\right)(4,13)$ is a particular solution of the given equation. The general solution is found using the formula from problem $\underline{60514}$.

b) $79 / 19=[4 ; 6,3] .[4 ; 6]=25 / 6$, so $(-6,-25)$ is a particular solution.

## Answer

a) $x_{k}=4+13 k, y_{k}=31+101 k(k \in \mathbf{Z})$; b) $x_{k}=-6+19 k, y_{k}=-25+79 k(k \in \mathbf{Z})$.