Euler Totient Function
Euler's totient function φ(n) counts the positive integers less than n and coprime to n; it is central to RSA cryptography.
Purpose
To count invertible elements under a modulus; the basis of RSA key generation and Euler's theorem.
Mechanism
If n=∏p_i^k_i, then φ(n)=n*∏(1-1/p_i). For a prime p, φ(p)=p-1. Multiplicative over coprime factors: φ(mn)=φ(m)*φ(n). In RSA, φ(N)=(p-1)(q-1).
Use cases
- RSA key generation
- Number-theoretic computation
- Modular arithmetic
Related tools
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Euler Totient Function
Euler Totient Function — pure client-side tool. Privacy-first, no server round-trip. TOOL