SUMMARY
The discussion focuses on finding the remainder of 34! divided by 37 using Wilson's Theorem, which states that for a prime p, (p-1)! ≡ -1 (mod p). Participants clarify that 34! can be expressed as 34! * 35 ≡ 1 (mod 37), leading to the equation 35x ≡ 1 (mod 37). The solution involves finding the modular multiplicative inverse of 35 modulo 37, ultimately determining that the remainder is 19. The extended Euclidean algorithm is recommended for solving similar modular equations.
PREREQUISITES
- Understanding of Wilson's Theorem
- Familiarity with modular arithmetic
- Knowledge of the extended Euclidean algorithm
- Basic skills in solving linear congruences
NEXT STEPS
- Study the application of Wilson's Theorem in combinatorial problems
- Learn about modular multiplicative inverses and their computation
- Explore the extended Euclidean algorithm in depth
- Practice solving linear congruences using various methods
USEFUL FOR
Mathematics students, particularly those studying number theory, educators teaching modular arithmetic, and anyone interested in combinatorial mathematics and its applications.