The Euler phi function, also known as Euler's totient function, is a mathematical function that counts the number of positive integers less than or equal to a given number that are relatively prime to it. It is denoted by φ (n).
The Euler phi function can be calculated using the formula φ (n) = n * (1 - 1/p1) * (1 - 1/p2) * ... * (1 - 1/pk), where n is the given number and p1, p2, ..., pk are its prime factors.
The Euler phi function has many applications in number theory and cryptography. It helps in determining the number of integers coprime to a given number, which is useful in solving various mathematical problems.
The Euler phi function is closely related to the prime factorization of a number. It uses the prime factors of a number to calculate the number of integers that are relatively prime to it.
No, the Euler phi function is defined only for positive integers. For negative integers, the value of the function is undefined. For 0, the value is 0.