Question 5 [Points 21]

1. [4 Points] Using Euclidean algorithm, determine GCD (132, 54 )
2. [5 Points] Find (450), the Eulers Phi function. (Note that 1,2,3,5, 7, etc. are the primes)
3. [6 points] Find the multiplicative inverse of 3 in GF(13) domain using Fermats Little theorem.
4. [6 points] Using Eulers theorem, find the following exponential: 4¹²³ mod 39. Show how you have employed Eulers theorem here.