Answered: (a) Does j ≡ k(mod n) imply a^j ≡…

(a) Does j ≡ k(mod n) imply a^j ≡ a^k(mod n) for all a ∈ Z? Justify your answer.(b) Does a ≡ b(mod n) imply a^i ≡ b^i(mod n) for all a, b ∈ Z, i ∈ Z+? Justify your answer.

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

(a) Does j ≡ k(mod n) imply a^j ≡ a^k(mod n) for all a ∈ Z? Justify your answer.
(b) Does a ≡ b(mod n) imply a^i ≡ b^i(mod n) for all a, b ∈ Z, i ∈ Z+? Justify your answer.

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