learn.howToCalculate
learn.whatIsHeading
Euler's totient function φ(n) counts how many integers from 1 to n are coprime to n (share no common factor other than 1). It is fundamental in number theory and RSA encryption.
公式
φ(n) = n × ∏(1 − 1/p) for all prime factors p of n; for prime p: φ(p) = p−1
- n
- positive integer
- φ(n)
- Euler totient of n — count of integers coprime to n
ステップバイステップガイド
- 1For prime p: φ(p) = p−1
- 2φ(pᵏ) = pᵏ−pᵏ⁻¹
- 3Multiplicative: φ(mn) = φ(m)φ(n) when gcd(m,n)=1
- 4φ(12) = φ(4)×φ(3) = 2×2 = 4
解いた例
入力
φ(12)
結果
4 (coprime: 1,5,7,11)
入力
φ(7)
結果
6 (prime: all 1–6 are coprime)
よくある質問
Why is φ(n) important in cryptography?
φ(n) is essential to RSA encryption: the security depends on the difficulty of computing φ for large products of primes.
What does "coprime" mean?
Two numbers are coprime if their greatest common divisor (GCD) is 1. They share no common factor except 1.
What is φ(p) for a prime p?
φ(p) = p−1, because all numbers 1 to p−1 are coprime to p.
計算する準備はできましたか?無料の Eulers Totient Function 計算機をお試しください
自分で試してみる→