I have the following question, please if able give explanation with the taken steps, I especially struggle with giving structure to my proof, knowing what to mention and what notthank you in advance a.b.C.Let n € Z. Show that n² = 1 (mod 3) if and only if 3 X n.Let n1, n2 € Z and m € IN. Show that n² = n² (mod m) whenever n₁ = n₂(mod m) or n₁ = −n₂ (mod m).Assume m = p is prime. Show conversely that n₁ = n₂ (mod p) or n₁ = −n2(mod p) whenever n = n (mod p).HINT/REMARK. You may use without proof the following result known as Euclid'sLemma: if p is prime and a, b are integers with plab, then pla or pb (or both).

Answered: Image /qna-images/answer/6541559c-77ed-4933-84f9-f956ba86d6eb.jpg

Answered: a. Let n E Z. Show that n² = 1 (mod 3)…

Math

Advanced Math

a. Let n E Z. Show that n² = 1 (mod 3) if and only if 3 X n.

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

I have the following question, please if able give explanation with the taken steps, I especially struggle with giving structure to my proof, knowing what to mention and what not

thank you in advance

a.
b.
C.
Let n € Z. Show that n² = 1 (mod 3) if and only if 3 X n.
Let n1, n2 € Z and m € IN. Show that n² = n² (mod m) whenever n₁ = n₂
(mod m) or n₁ = −n₂ (mod m).
Assume m = p is prime. Show conversely that n₁ = n₂ (mod p) or n₁ = −n2
(mod p) whenever n = n (mod p).
HINT/REMARK. You may use without proof the following result known as Euclid's
Lemma: if p is prime and a, b are integers with plab, then pla or pb (or both).

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