Number theory is a branch of pure mathematics devoted to the study of the integers and integer-valued functions, exploring properties such as divisibility, prime numbers, and the solutions to equations in integers. It has deep connections with other areas of mathematics and finds applications in cryptography, computer science, and mathematical puzzles.

Number Theory

Number theory

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. It is driven by abstract problems and the intrinsic beauty of mathematical structures, often leading to discoveries that later find practical applications.

pure mathematics

Integers are a fundamental number set in mathematics, consisting of whole numbers and their negatives, including zero. They are used extensively in various mathematical operations and are crucial for understanding more complex number systems and algebraic structures.

integers

integer-valued functions

Divisibility is a fundamental concept in number theory that determines whether one integer can be divided by another without leaving a remainder. Understanding divisibility helps in simplifying fractions, finding greatest common divisors, and solving problems involving modular arithmetic.

divisibility

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves, serving as the building blocks of number theory. They play a crucial role in various fields, including cryptography, due to their properties and distribution patterns.

prime numbers

equations in integers

applications in cryptography

Computer science is the study of algorithmic processes, computational machines, and computation itself, which underpins the development of software and systems that drive modern technology. It encompasses a wide range of topics from theoretical foundations to practical applications, making it essential for innovation in various fields such as artificial intelligence, cybersecurity, and data science.

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