The question is "find the smallest solution to the indeterminate equation $195y = 221x + 65$ using the Indian method of kuttaka."
Factoring out $13$, I got $15y = 17x + 5$
Using kuttaka, I got $x = 35$ and $y = 40$, which works, but apparently the smallest answer is $x = 5$ and $y = 6$.
How do you find the smallest possible values for $x$ and $y$?
Thanks.
Once you already have a solution set $(x_0,y_0)$ to $ax-by=n$, then you also have $(x_0+bk,y_0+ak)$ as solutions (you can check that this doesn't change the value). So all you need to do is find the minimum $k$ where $(x_0+bk,y_0+ak)$ is still positive.