Can someone explain how wolfram alpha calculates integer solutions for these kind of equations:

$$ m=\frac{681+13973k}{2021} $$

and how can I do this myself on the paper?

Here is a link to the wolfram alpha solution:


where it shows the integer solution at the bottom.



I think they use congruence relation and Euclidean procedure for finding gcd (greatest common divisor).


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