Introduction to Euler’s Totient Function (φ) Definition, Types, Examples & Uses

Introduction to Euler’s Totient Function (φ)

Subject: Mathematics

Book: Maths Mastery

Euler’s Totient Function φ(n) counts how many integers ≤n are coprime to n. For prime p, φ(p)=p–1. For example, φ(8)=4 because only {1,3,5,7} are coprime with 8. This function is core in number theory and cryptography (Euler’s theorem, RSA encryption). Euler’s theorem states a^φ(n)≡1 (mod n) if gcd(a,n)=1. Understanding φ fosters advanced integer analysis, letting you compute exponents mod n or analyze prime-based structures. Mastery in totient calculations links to deeper insights in modern computer security and theoretical math.