I have the following questions, please if able write it step by step with explanation, thank in advance b.C.Let n1, n2 € Z and m € IN. Show that n² = n3 (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 n² = n² (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/0c133748-1583-4b64-a2aa-40fd33afc1d7.jpg

Answered: b. Let n1, n2 € Z and m € IN. Show that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

I have the following questions, please if able write it step by step with explanation, thank in advance

b.
C.
Let n1, n2 € Z and m € IN. Show that n² = n3 (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 n² = n² (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).

Expert Solution

Step 1: Step 1

$b. space L e t space n subscript 1 identical to n subscript 2 space left parenthesis m o d space m right parenthesis. T h e n space open parentheses n subscript 1 minus n subscript 2 close parentheses vertical line m. N o w space n subscript 1 squared minus n subscript 2 squared equals open parentheses n subscript 1 minus n subscript 2 close parentheses open parentheses n subscript 1 plus n subscript 2 close parentheses. open parentheses n subscript 1 minus n subscript 2 close parentheses vertical line m rightwards double arrow open parentheses n subscript 1 minus n subscript 2 close parentheses open parentheses n subscript 1 plus n subscript 2 close parentheses vertical line m i. e space n subscript 1 squared minus n subscript 2 squared vertical line m rightwards double arrow space n subscript 1 squared identical to n subscript 2 squared space left parenthesis m o d space m right parenthesis.$