A square-free integer is a positive integer that is not divisible by any perfect square other than 1, meaning it has no repeated prime factors. This property makes square-free integers important in number theory, especially in the study of factorization and the distribution of prime numbers.

Square-free Integer

square-free integer

positive integer

A perfect square is an integer that is the square of another integer, meaning it can be expressed as n² where n is an integer. Perfect squares have an odd number of total divisors and their square roots are always whole numbers.

perfect square

repeated 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

Factorization is the process of breaking down an expression or number into a product of its factors, which are simpler elements or numbers that multiply together to form the original. This concept is fundamental in mathematics, particularly in solving equations, simplifying expressions, and finding greatest common divisors or least common multiples.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

Relevant Fields: