Answered: Prove, that if 2m + 1 is a prime…

Prove, that if 2m + 1 is a prime number, then m must be a power of 2 (m = 2n, for some n ∈ N). Prime numbers in the form p = 2m + 1 are called Fermat's prime numbers. Plz write clearly.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 19E: Prove that if n is a positive integer greater than 1 such that n is not a prime, then n has a...

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Question

Prove, that if 2^m + 1 is a prime number, then m must be a power of 2 (m = 2ⁿ, for some n ∈ N).
Prime numbers in the form p = 2^m + 1 are called Fermat's prime numbers.

Plz write clearly.

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