18) Let a, b, and n be positive integers, with $d = gcd(a, b)$, $a = da'$, $b = db'$. Show that the general solution of
$ax + by = nd$ is of the form $x = x_0 - kb'$, $y = y_0 + ka'$, with $k \in \mathbb{Z}$ where $(x_0, y_0)$ is a particular solution of
$a'x_0 + b'y_0 = n$ (we solved this problem in the case of $n = 1$ in the class, please follow a similar procedure but this
time start with $nd$ in the right hand side of your equation).
19) Find the general solution of $39x + 144y = 6$ where x, y are integers.
20) Find the general solution of $12x + 40y = 8$ where x, y are integers.
