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What is the modular multiplicative inverse

Assignment: Extended Euclidean Algorithm

Using any programming language of your choice implement the Extended Euclidean algorithm

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?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.

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