p-adic numbers are a system of numbers used in number theory, developed by mathematician Kurt Hensel in the early 20th century. They extend the concept of integers and rational numbers by focusing on the divisibility of numbers by a prime number p. In this system, numbers are represented in a way that emphasizes their behavior under division by p, allowing for a different perspective on convergence and limits. The p-adic system is built on the idea of a p-adic metric, which measures the distance between numbers based on their divisibility by p. This leads to unique properties, such as the ability to represent numbers that are infinitely close to each other in the p-adic sense, even if they differ significantly in the usual sense. This framework has applications in various areas of mathematics, including algebraic geometry and cryptography.