Let k be a positive integer. Prove that if 2k +1 is prime, then k = 2". The integer F₁ = 22" +1 is called the nth Fermat number. Primes of the form 22" +1 are called Fermat primes. Show that F₁ is prime for n = 1, 2, 3, 4.
Let k be a positive integer. Prove that if 2k +1 is prime, then k = 2". The integer F₁ = 22" +1 is called the nth Fermat number. Primes of the form 22" +1 are called Fermat primes. Show that F₁ is prime for n = 1, 2, 3, 4.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 42E
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![Let k be a positive integer. Prove that if 2 + 1 is prime, then k = 2".
The integer
F₁ = 2²" + 1
is called the nth Fermat number. Primes of the form 22" +1 are called
Fermat primes. Show that F, is prime for n = 1, 2, 3, 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30761ad5-6d22-4ff4-adb6-4f166a7ab52a%2Fed5716ba-4719-4a1f-8322-2d93270c3ed0%2F1cyz5wu.jpeg&w=3840&q=75)
Transcribed Image Text:Let k be a positive integer. Prove that if 2 + 1 is prime, then k = 2".
The integer
F₁ = 2²" + 1
is called the nth Fermat number. Primes of the form 22" +1 are called
Fermat primes. Show that F, is prime for n = 1, 2, 3, 4.
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