g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19

Step-by-step explanation:

Solving (a): 241^257 mod 12

To do this, we simply calculate

Because

The highest number less than or equal to 241 that is divisible by 12 is 240; So:

Hence:

Solving (b): 7 * 20

Solving (c): Multiplicative inverse of 7 in 719

The position of 7 in 719 is 700

So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number

1/800 is the right answer