p-adic numbers

P-adic numbers are a way of extending the ordinary numbers to analyze properties related to divisibility by a prime number p. Instead of focusing on size or distance as usual, p-adic numbers measure how divisible a number is by p—more divisible means "closer" in this system. This creates a new number system where sequences that grow increasingly divisible by p converge to a p-adic number. They are useful in number theory for solving equations and understanding properties of integers in relation to a specific prime, offering a different perspective compared to real numbers.