Question: 1) Using any programming language of your choice implement the Extended Euclidean algorithm
2) Specifications: The program should take two inputs 1) An integer a, which is the modulus 2) A non-negative integer b that is less than a. The program should output three values 1) gcd(a,b) 2) Integer x and 3) Integer y, such that ax + by = gcd(a,b)
Test 1: 1) Run your program with a = 1759 b = 550
2) What are your outputs?
3) What is the modular multiplicative inverse of 550 mod 1759?
Test 2: 1) Run your program with a = 43 b = 17
2) What are your outputs?
3) What is the modular multiplicative inverse of 17 mod 43? Note that the modular multiplicative inverse has to be non-negative and less than 43.
Test 3: 1) Run your program with a = 400 b = 10
2) What are your outputs?
3) What is the modular multiplicative inverse of 10 mod 400? Be mindful of the gcd value to answers this question