Extended Euclidean algorithm


1) Using any programming talk of your exquisite utensil the Extended Euclidean algorithm 

2) Specifications: The program should interest two inputs 1) An integer a, which is the modulus 2) A non-negative integer b that is near than a. The program should output three appreciates 1) gcd(a,b) 2) Integer x and 3) Integer y, such that ax + by = gcd(a,b)  

Test 1 

1) Run your program delay 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 delay 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 near than 43. 

Test 3 

1) Run your program delay a = 400 b = 10 

2) What are your outputs? 

3) What is the modular multiplicative inverse of 10 mod 400? Be attentive of the gcd appreciate to answers this question