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 ...

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 ...

For novices, functions are one of the most intimidating features of OpenOffice.org's Calc. Newcomers quickly learn that functions are a main feature of spreadsheets, but there are almost four hundred, ...

Scientists have developed and demonstrated the world's first programmable nanoprocessor. The groundbreaking prototype computer system represents a significant step forward in the complexity of ...

Here's why math fact fluency matters, and what we know from research about teaching strategies and timed exercises.

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...