The appearance of combinatorial problems may be traced back far into
time. In a letter considered to have been addressed by Archimedes to
Eratosthenes, it is proposed, subject to certain conditions, to \compute the
number of cattle of the Sun." This problem is one of the rare allusions in
antiquity to combinatorics and its confrontation depends on consideration
of the polygonal numbers of Pythagoras, Nicomachos and Diophantos.