I'm quite new to number theory and I'm studying diophantine equations. I noticed that the technique was used for solving integer solutions. However, what technique can I use for solving natural number solutions?
For example, $ax + by = c$ find natural number solutions for $a$ and $b$
The only guess I can come up with is to set x and y to be absolute value:
$a|x| + b|y| = c$
But I'm not really sure how to solve this. Is there any other way I can go about finding only natural number solutions? Any help would be appreciated, thank you!