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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

Sagot :

MrRoyal

Answer:

[tex]241^{257}\ mod\ 12 =1[/tex]

[tex]7 * 20 = 140[/tex]

[tex]\frac{1}{700}[/tex]

Step-by-step explanation:

Solving (a): 241^257 mod 12

To do this, we simply calculate [tex]241\ mod\ 12[/tex]

Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]

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

[tex]241\ mod\ 12 = 241- 240[/tex]

[tex]241\ mod\ 12 =1[/tex]

Hence:

[tex]241^{257}\ mod\ 12 =1[/tex]

Solving (b): 7 * 20

[tex]7 * 20 = 140[/tex]

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

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