  The existence of certain monomial hyperovals $D(x^k)$ in the finite
Desarguesian projective plane $PG(2,q)$, $q$ even, is related to the existence
of points on certain projective plane curves $g_k(x,y,z)$. Segre showed that
some values of $k$ ($k=6$ and $2^i$) give rise to hyperovals in $PG(2,q)$ for
infinitely many $q$. Segre and Bartocci conjectured that these are the only
values of $k$ with this property. We prove this conjecture through the absolute
irreducibility of the curves $g_k$.
