Question

1. Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11

2. Use the max function to calculate max3(x, y, z) if x = 2, y = 6, z = 5. Show your work!

Answer 1

1. First lets apply the algorithm. It will verify that gcd(8,11) = 1.

11 = 8(1) + 3

8 = 3(2) + 2

3 = 2(1) + 1

2 = 1(2)

Now solve for remainders,

3 = 11 - 8(1)

2 = 8 - 3(2)

1 = 3 - 2(1)

Now reverse the process using these equations,

1 = 3 - 2(1)

1 = 3 - (8 - 3(2)) (1)

1 = 3 - (8 - (3(2))

1 = 3(3) - 8

1 = (11 - 8(1) )(3) - 8

1 = 11(3) - 8(4)

1 = 11(3) + 8(-4)

Therefore 1 ≡ 8(−4) mod 11, or if you want to prefer a residue value for f^-1,

1 ≡ 8(7) mod 11.

2. As the programming language is not mentioned so I am doing it in C++. Let's define a max3(x,y,z) function which will calculate the maximum of 3 values.

int max3(int x, int y, int z)

{

int largest = x;

if(largest < y)

largest = y;

if(largest < z)

largest = z;

else

return largest.

}

This function will find the largest of three numbers.

If you want to use the by-default function max(), you can prefer Python language as it simply provides a by-default function to calculate the largest of the given numbers.

If you still have any doubt/query regarding the solution then let me know in comment. If it helps, kindly give an upVote to this answer.