On Reid conjecture of score sets for tournaments (Q1262874)

\textit{K. B. Reid} [Proc. 9th Southeast. Conf. Combinatorics, Graph Theory, and Computing, Boca Raton 1978, Congressus numerantium XXI, Utilitas Math. 607-618 (1978; Zbl 0414.05022)] proposed that every finite and nonempty set S of positive integers is the score (outdegree) set for some tournaments and proved the conjecture for sets of cardinality less than four. Here the author gives a proof of the conjecture verifying Landau's condition for a score sequence [\textit{H. G. Landau}, Bull. Math. Biophysics 15, 114-118 (1953)] using number-theoretical arguments.