Euler's Theorem is a cornerstone in number theory, stating that for any two integers a and n that are coprime, the following holds:
a^φ(n) ≡ 1 mod n, where φ(n) is Euler's totient function. 📐✨

🧠 Key Concepts

  • Coprime Numbers: Two numbers with no common divisors other than 1.
  • Totient Function φ(n): Counts integers up to n that are coprime with n.
  • Modular Arithmetic: Central to the theorem's application in cryptography and algorithms.

🔍 Applications

  • RSA Encryption: Used in public-key cryptography for secure data transmission.
  • Graph Theory: Applies to Eulerian circuits in network analysis.
  • Number Theory: Simplifies calculations in modular systems.

📚 History

  • Proposed by Leonhard Euler in 1760.
  • Builds on Fermat's Little Theorem, extending it to composite moduli.
Euler_Theorem

For deeper exploration, check our guide on number theory fundamentals. 🌐🧮

Eulerian_Circuit