Modern number theory

Modern number theory is a branch of mathematics that studies the properties and relationships of numbers, particularly integers. It explores concepts like prime numbers, which are numbers greater than one that have no divisors other than one and themselves. The field delves into patterns, distribution, and the mysterious connections between numbers, often using advanced techniques from algebra and geometry. Important questions include understanding how primes are distributed or solving equations that involve whole numbers. Modern number theory has applications in cryptography, computer science, and beyond, making it a vital area of research with practical importance.