2 problems

Let $R(k)=\frac{3k^2-3k}{2}$. Let $\mathcal{C}$ be a non-singular real algebraic curve of degree $2k$ in $\mathbb{P}^2$, with $p$ even ovals and $n$ odd ovals. Ragsdale's conjectur…

Let $R(k)=\frac{3k^2-3k}{2}$. For a non-singular real algebraic curve $\mathcal{C}$ of degree $2k$ in $\mathbb{P}^2$, let $p$ and $n$ denote the numbers of even and odd ovals, resp…