Problem 7 Show that if 2" - 1 is prime then n is prime. Hint: Use the identity 2ab1 = (2-1) (2a(b-1) + 2a(b-2) +...+ 2ª + 1)
Problem 7 Show that if 2" - 1 is prime then n is prime. Hint: Use the identity 2ab1 = (2-1) (2a(b-1) + 2a(b-2) +...+ 2ª + 1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 72E
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![**Problem 7: Show that if \(2^n - 1\) is prime then \(n\) is prime.**
*Hint:* Use the identity
\[2^{ab} - 1 = (2^a - 1)(2^{a(b-1)} + 2^{a(b-2)} + \cdots + 2^a + 1)\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe872339c-719c-4a81-bc7c-37653a99cb41%2F7f992471-bc37-4019-bde7-5c648605922a%2Fzjjw1p7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7: Show that if \(2^n - 1\) is prime then \(n\) is prime.**
*Hint:* Use the identity
\[2^{ab} - 1 = (2^a - 1)(2^{a(b-1)} + 2^{a(b-2)} + \cdots + 2^a + 1)\]
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