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 not 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 not
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.
Transcribed Image Text: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 not 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.
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