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 an M-curve of even degree obeys the congruence
where is the number of positive ovals and 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 , where is the number of maximal components of the curve.[1])
The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.[2][3][4]