p-adic number theory is a branch of mathematics that extends the concept of numbers beyond the familiar real and complex numbers. It focuses on the p-adic numbers, which are defined for a prime number p. These numbers allow mathematicians to study properties of integers and rational numbers in a new way, particularly in relation to divisibility and congruences. In p-adic number theory, distances between numbers are measured differently than in traditional number systems. This leads to unique insights in areas such as algebraic number theory and modular forms. The theory has applications in various fields, including cryptography and mathematical logic.