For the following prime p and number a, compute a−1 mod p in two ways: (i) Use the extended Euclidean algorithm. (ii) Use the fast power algorithm and Fermat’s little theorem. Where p = 104801 and a = 78467.

For the following prime p and number a, compute a−1 mod p in two ways: (i) Use the extended Euclidean algorithm. (ii) Use the fast power algorithm and Fermat’s little theorem. Where p = 104801 and a = 78467.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 34E

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Question

For the following prime p and number a, compute a−1 mod p in two
ways: (i) Use the extended Euclidean algorithm. (ii) Use the fast power algorithm
and Fermat’s little theorem. Where p = 104801 and a = 78467.

Expert Solution