Fermat's "Little" Theorem states that whenver n is prime and a is an integer, d"-1 = 1 mod n a) If a = 133 and n = 157, then efficiently compute 133156 = 1 mod 157 b) If a = 25 and n = 97, then efficiently compute 25 · 2595 = 1 mod 97 Use the Extended Euclidean Algorithm to compute 25- = -31 mod 97. Then 259 = 8 mod 97. c) If a = 152 and n = 463, then efficiently compute 152464 mod 463 II

Fermat's "Little" Theorem states that whenver n is prime and a is an integer, d"-1 = 1 mod n a) If a = 133 and n = 157, then efficiently compute 133156 = 1 mod 157 b) If a = 25 and n = 97, then efficiently compute 25 · 2595 = 1 mod 97 Use the Extended Euclidean Algorithm to compute 25- = -31 mod 97. Then 259 = 8 mod 97. c) If a = 152 and n = 463, then efficiently compute 152464 mod 463 II

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.6: Congruence Classes

Problem 25E

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