High Quality Content by WIKIPEDIA articles! In algebraic geometry, a field of mathematics, the AF+BG theorem is a result of Max Noether which describes when the equation of an algebraic curve in the complex projective plane can be written in terms of the equations of two other algebraic curves. This theorem provides an analog for polynomials of Bezout's identity, which provides a condition under which an integer h can be written as a sum of integer multiples of two other integers f and g: such a representation exists exactly when h is a multiple of the greatest common divisor of f and g. The AF+BG condition expresses, in terms of divisors (sets of points, with multiplicities), a similar condition under which a polynomial H can be written as a sum of polynomial multiples of two other polynomials F and G.

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