  The aim of the present article is to explore the possibilities of
representing positive integers as sums of other positive integers and highlight
certain fundamental connections between their multiplicative and additive
properties. In particular, we shall be concerned with the representation of
positive integers as arithmetic series of the simplest kind, i.e., either as
sums of successive odd positive numbers, or as sums of successive even positive
numbers (both treated as Problem 1), or as sums of consecutive positive
integers (treated as Problem 2).
