Two integers are relatively prime if their greatest common divisor is 1, meaning they share no prime factors. This property is fundamental in number theory and is essential for understanding concepts such as coprime numbers, modular arithmetic, and the Euler's totient function.

Relatively Prime

Two integers

relatively prime

The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. It is a fundamental concept in number theory and is essential for simplifying fractions and solving Diophantine equations.

greatest common divisor

prime factors

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

coprime numbers

Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after reaching a certain value, known as the modulus. It is fundamental in number theory and is widely used in computer science, cryptography, and coding theory for its properties of periodicity and equivalence classes.

modular arithmetic

Euler's Totient Function, denoted as φ(n), is a fundamental function in number theory that counts the positive integers up to a given integer n that are relatively prime to n. It plays a crucial role in Euler's theorem, which is a generalization of Fermat's Little Theorem and is pivotal in cryptographic algorithms like RSA.

Your Courses

Relevant Degrees

Your Lessons