1. Prove the following statement:If for some n € Z>1, 2" – 1 is prime then n is prime.by both contradiction and contrapositive.Hint. Let x, n € Z>o and let 1 ≤ k ≤n, 1 ≤l≤n with n= kl. Then (x-1) is composite:(x¹ − 1) = (x² − 1) (xl(k-1) + xl(k-2) +...x² +1).

Given statement: Statement 1: For some n∈ℤ+, 2n-1 is prime. Statement 2: n is prime. Prove that…

Answered: Prove the following statement: If for…

Prove the following statement: If for some ne Z>1, 2" - 1 is prime then n is prime. by both contradiction and contrapositive.

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

1. Prove the following statement:
If for some n € Z>1, 2" – 1 is prime then n is prime.
by both contradiction and contrapositive.
Hint. Let x, n € Z>o and let 1 ≤ k ≤n, 1 ≤l≤n with n= kl. Then (x-1) is composite:
(x¹ − 1) = (x² − 1) (xl(k-1) + xl(k-2) +...x² +1).

Expert Solution

Step 1

Given statement:

Statement 1: For some $n \in ℤ^{+}$ , $2^{n} - 1$ is prime.

Statement 2: $n$ is prime.

Prove that statement 1 is true then statement 2 is true.

Method to prove:

i) Contradiction.

ii) Contrapositive.

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