Extended Euclidean algorithm

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 

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