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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.

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    It's called a *mixed fraction*. $\dfrac{4238 - 97y}{95} = 44 \ \ \dfrac{58}{95} - (1 \ \ \dfrac{2}{95})y$2012-04-19

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It's just a funny way to call a pretty elementary arithmetic operation: $\frac{4238-97y}{95}=\frac{44\cdot 95+58-(95y)-2y}{95}=\frac{44\cdot 95}{95}-\frac{95y}{95}+\frac{58-2y}{95}=$ $=44-y+\frac{58-2y}{95}$

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    Yup, yet the OP just asked about the process the page he linked to was carrying out. Apparently, and hopefully, he can follow the rest of the argument2012-07-04