Problem

Source: Iranian National Olympiad (3rd Round) 2007

Tags: algebra, polynomial, geometry, function, algebra proposed



Prove that for two non-zero polynomials $ f(x,y),g(x,y)$ with real coefficients the system: \[ \left\{\begin{array}{c}f(x,y)=0\\ g(x,y)=0\end{array}\right.\] has finitely many solutions in $ \mathbb C^{2}$ if and only if $ f(x,y)$ and $ g(x,y)$ are coprime.