Solution
= Solution
The strong <Bézout theorem> says that if two projective plane <algebraic curves> $C,D$ over $\mathbb C$ have degrees $m,n$ and no common irreducible component, their intersection is finite and
$$
\boxed{\sum_{p\in C\cap D}I_p(C,D)=mn.}
$$
Each <intersection multiplicity> is a positive integer. Scheme-theoretic multiplicities, rather than just distinct intersection points, are essential: tangencies and singularities can make individual terms larger than one.