On \(p\)- and \(q\)-additive functions
The paper attempts to describe those arithmetic functions that are simultaneously \(p\)- and \(q\)-additive for two integers \(p, q\) which are not powers of a common integer. It is proved that the function is a sum of a linear and a periodic function, whose period is of the form \((p^l, q^m)\). In particular, if \(p,q\) are coprime, the function must be linear. A similar result is given for \(p\)- and \(q\)-multiplicative functions. These results extend those of \textit{T. Toshimitsu} [Tokyo J. Math. 21, 107-113 (1998; Zbl 0906.11036)], where strongly \(q\)-additive and multiplicative functions were considered.
scientific article; zbMATH DE number 1340489