You may never have heard of modular arithmetic, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is ...

Arithmetic geometry and p-adic differential equations form a dynamic nexus where number theory, algebraic geometry and p-adic analysis converge. This interdisciplinary field investigates the solutions ...

Research into the cryptanalysis of RSA and modular equations has seen significant evolution in recent years. The RSA cryptosystem, long revered for its robust security based on the computational ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

One of my fellow contributors here recently wrote a post about leap years and why we have them. This reminded me of modular arithmetic and the formula for calculating the day of the week for any date ...

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine ...