Wikipedia tells me about Max Noether's $AF + BG$ theorem but only gives one reference and one external link. I've had a look at the MathWorld link but it seems to be an entirely geometric formulation which I'm not even sure is the same theorem. Does anyone know where I can find an algebraic statement of the theorem, together with a proof? I've tried searching online but the name of the theorem is somewhat unfortunate...
You can find it in Fulton's wonderful book - algebraic curves, available online here: http://people.reed.edu/~davidp/332/CurveBook.pdf page 61 (page 69 in the above file).