In this booklet, Prof. Kaluzhnin deals with one of the fundamental propositions of arithmetic of rational whole numbers â the uniqueness of their expansion into prime multipliers. Having established a conncetion between arithmetic and Gaussian numbers and the question of representing integers as sum of squares, Prof. Kaluzhnin has shown the uniqueness of expansion also holds in the arithmetic of complex (Gaussian) whole numbers. The author hopes that the booklet will not only be of interest to senior schoolboys but will also be useful for teachers.