Problem 1: (a) Compute 13-¹ (mod 23) by enumerating multiples. Show your work. (b) Compute 13-1 (mod 23) using Fermat's Little Theorem. Show your work. (c) Compute 11-11 (mod 19) using Fermat's Little Theorem. Show your work. (d) Use Fermat's Little Theorem to compute 71209643 (mod 11). Show your work. (e) Find an integer x, 0≤x≤ 40, that satisfies 31x + 42 = 4 (mod 41). Show your work. You should no use brute force approach. (f) Calculate 138-1 (mod 2784) using any method of your choice. Show your work. (g) How many integers have inverses modulo 144? Justify.
Problem 1: (a) Compute 13-¹ (mod 23) by enumerating multiples. Show your work. (b) Compute 13-1 (mod 23) using Fermat's Little Theorem. Show your work. (c) Compute 11-11 (mod 19) using Fermat's Little Theorem. Show your work. (d) Use Fermat's Little Theorem to compute 71209643 (mod 11). Show your work. (e) Find an integer x, 0≤x≤ 40, that satisfies 31x + 42 = 4 (mod 41). Show your work. You should no use brute force approach. (f) Calculate 138-1 (mod 2784) using any method of your choice. Show your work. (g) How many integers have inverses modulo 144? Justify.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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