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.