Euler's Totient Function Calculator
Calculate Euler's totient function φ(n) and find coprime integers
About this calculator
Euler's Totient Function Calculator computes φ(n), which counts the positive integers up to n that are relatively prime to n (share no common factors except 1). This fundamental number theory function is essential in cryptography, particularly RSA encryption, and mathematical research. The calculator also identifies all coprime integers within the specified range, making it valuable for students studying number theory, researchers working with modular arithmetic, and professionals implementing cryptographic algorithms.
How to use
Enter any positive integer n into the input field and click calculate. The calculator will compute φ(n) and display the result along with a complete list of all integers from 1 to n that are coprime to your input number. The result shows both the count and the actual coprime values.
Frequently asked questions
What does it mean for numbers to be coprime?
Two numbers are coprime if their greatest common divisor (GCD) is 1, meaning they share no common prime factors except 1.
Why is Euler's totient function important in cryptography?
φ(n) is crucial for RSA encryption key generation, as it determines the number of valid encryption exponents for a given modulus.
What is φ(1) and why?
φ(1) equals 1 because the only positive integer ≤ 1 is 1 itself, and gcd(1,1) = 1, making them coprime by definition.