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 ...

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 ...

Let d(n), respectively σ(n), stand for the number, respectively the sum, of the positive divisors of n, and let φ be Euler's totient function. Also let d₃(n) be the number of solutions of a₁a₂a₃ = n ...

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 ...

The researchers discovered that this separation proves remarkably clean. In a preprint paper released in late October, they ...

Researchers at Aalto University have demonstrated single-shot tensor computing at the speed of light, a remarkable step ...

Microsoft's Excel program, widely used in business, comes with many built-in functions that perform mathematical and logical operations on spreadsheet data. In Excel, functions are simple formulas you ...

Researchers studying how large AI models such as ChatGPT learn and remember information have discovered that their memory and ...