Gudkov's conjecture

In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after D. A. Gudkov) was a conjecture, and is now a theorem, which states that "a M-curve* of even degree 2d obeys p – n ≡ d² (mod 8)", where p is the number of positive ovals and n the number of negative ovals of the M-curve. It was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.