SUMMARY
The discussion centers on the relationship between the number m, defined as the product of two prime numbers p and q, and Euler's Totient Function, Φ(m). It is established that if m = pq, then Φ(m) = (p-1)(q-1). The key insight is that knowing both m and Φ(m) allows for the deduction of p and q through the quadratic equation x² - Sx + m = 0, where S = m - Φ(m) + 1 = p + q. This method avoids brute force factorization.
PREREQUISITES
- Understanding of Euler's Totient Function
- Knowledge of quadratic equations
- Familiarity with prime factorization
- Basic algebra skills
NEXT STEPS
- Study the properties of Euler's Totient Function in depth
- Learn about quadratic equations and their solutions
- Explore advanced factorization techniques beyond brute force
- Investigate cryptographic applications of prime factorization
USEFUL FOR
Mathematicians, cryptographers, computer scientists, and anyone interested in number theory and efficient factorization methods.