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

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

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal component. Integers are fundamental in mathematics as they form the basis of various number systems and are used in numerous mathematical operations and theories.

integer

Simplifying fractions involves reducing the numerator and denominator to their smallest whole numbers while maintaining the same value of the fraction. This process is achieved by dividing both the numerator and denominator by their greatest common divisor (GCD), ensuring the fraction is in its simplest form.

simplifying fractions

greatest common divisors

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.

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