Let A = {x e Z: (7x + 39) mod 17 = 14}. a) Find a number ß such that (7B) mod 17 = 1. b) Prove that there exists a number z e {0, 1, ..., 16) such that A = {x € Z:x mod 17 = z}. c) Find z. (Hint: Use modular arithmetic.)

Let A = {x e Z: (7x + 39) mod 17 = 14}. a) Find a number ß such that (7B) mod 17 = 1. b) Prove that there exists a number z e {0, 1, ..., 16) such that A = {x € Z:x mod 17 = z}. c) Find z. (Hint: Use modular arithmetic.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let
A = {x € Z: (7x + 39) mod 17 = 14}.
a) Find a number ß such that (7B) mod 17 = 1.
b) Prove that there exists a number z e {0, 1, ..., 16} such that
A = {x € Z :x mod 17 = z}.
c) Find z.
(Hint: Use modular arithmetic.)

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