In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that a M-curve of even degree
the number of negative ovals of the M-curve.
(Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is
is the number of maximal components of the curve.
[1]) The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.