Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...

Recent investigations probe the arithmetic properties of these functions, exploring congruence relations and modular behaviour that reveal surprising regularities.

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...