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 ...

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 ...

Quadratic equations are polynomials, meaning strings of math terms. An expression like “x + 4” is a polynomial. They can have one or many variables in any combination, and the magnitude of them is ...

Polynomial Identity Testing (PIT) is a central problem in this arena, involving the efficient determination of whether a given arithmetic circuit computes the zero polynomial.