1. Find the additive and multiplicative inverses for the residual sets Z13, Z14, and Z11. Identify...

1. Find the additive and multiplicative inverses for the residual sets Z13, Z14, and Z11. Identify each as being a group, ring or field

2. Write an algorithm for performing Euclid greatest common denominator for A,B in Matlab and demonstrate the results for A=9777 and B=106665. Compare this the the matlab function gcd(A,B) and the by hand.

3. Program Euclid’s Extended algorithm in Matlab and demonstrate on the residual sets in problem 1.

4. Demonstrate Fermats and Eulers Theorems with the value of a set to the Residual set Z13 and Z14 and with P equal to 13 and 14 respectively. Explain results

5. Perform the Chinese Remainder theorem as in the example in your text with m1=29, m2=47

Expert Solution

Colby Messinger answered 8 hours ago

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