by   S.Yu. Orevkov   and   O.Ya. Viro

Abstract: We prove the congruence  p - n = k (k - 1) mod 8  for M-curves in RP² of odd degree   2k + 1 = 4 d + 1  with 4 nests of depth  d  where  p  and  n  is thenumber of even and odd ovals.  We derive this from Kharlamov-Viro congruence for singular curves. For  d = 2,  this is equivalent to the fact (conjectured by Korchagin) that the number of exterior empty ovals of a curve of degree  9  with  4  nests is divisible by  4.