On new theorems for elementary number theory

Introduction: This paper* generalizes the classical number-theoretic notions of multiplicative function and additive function. In addition to extending classes of functions it can be shown that certain specific functions such as, e.g., Euler's totient, Mόbius' function, and Liouville's function have precise analogues within the theory. Results of G. H. Hardy and S. Ramanujan are used in the study.