We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger
than one.
Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c
natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see
\cite{rg}). In this paper we prove an extension of Mordell's theorem and
formulate a conjecture which is stronger than Erdos' conjecture.