I would like to find some positive integer solutions to an equation in the form $Ax + By = C.$ I have already seen some methods for doing this, such as the one outlined in this Math.SE post.
What I am interested in is the method shown here. The first example is the one I was looking at. I can follow it up to fig [1.2]. I don't understand what the author means by "Reducing the right-hand side to integers and fractions." I would greatly appreciate some help in understanding this process. Also, is there a name that I can Google for the method used in this article? Thanks.
It's just a funny way to call a pretty elementary arithmetic operation: $$\frac{4238-97y}{95}=\frac{44\cdot 95+58-(95y)-2y}{95}=\frac{44\cdot 95}{95}-\frac{95y}{95}+\frac{58-2y}{95}=$$ $$=44-y+\frac{58-2y}{95}$$