Using the extended Euclidean algorithm, find the multiplicative inverses of (a) 1234 (mod 4321), (b) 550 (mod 769). Show the calculations.
Exercise: Use the repeated squaring method to calculate each of the following (show the IDAI steps for each calculation): 37 (mod 12), 160 (mod 230), 514 (mod 26), 422 (mod 11), 365 (mod 71). Answer:
Exercise: Use Fermat's Little Theorem (and other methods if needed) to calculate the following (all moduli are prime numbers): 99101 (mod 101), 9466 (mod 67), 49687327510 (mod 7541), 65441 (mod 73), 6543 (mod 73). Show and explain the main steps.