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Bézout's **theorem** is named after the French mathematician Etienne Bézout, who stated and gave a (partially correct) **proof** of the result in 1779. The statement itself is much much older, appearing in the works of Jacques Bernoulli, **Colin Maclaurin**, and others. The result deals with plane algebraic curves, which are subsets of the plane defined as the solution set of an equation f(x,y)=0, where f(x,y) is a polynomial in two variables. The total degree of the polynomial is called the degree of the curve. Bézout's theorem then states that two plane algebraic curves of degrees m and n intersect in at most mn points unless they have a common component; that is, unless there exists an algebraic curve which is a subset of both curves.

There is a more precise version of the...

This section contains 451 words(approx. 2 pages at 300 words per page) |