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# Fermat primes are prime numbers that can be written in the form 2^k+1

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
Fermat primes are prime numbers that can be written in the form 2^k+1  [#permalink]

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16 Sep 2018, 21:25
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Difficulty:

5% (low)

Question Stats:

100% (00:45) correct 0% (00:00) wrong based on 39 sessions

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Fermat primes are prime numbers that can be written in the form $$2^k+1$$, where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

A. 3
B. 5
C. 17
D. 31
E. 257

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Joined: 18 Aug 2017
Posts: 179
Concentration: Healthcare, Marketing
Re: Fermat primes are prime numbers that can be written in the form 2^k+1  [#permalink]

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16 Sep 2018, 21:32
1
Fermat primes are prime numbers that can be written in the form 2k+12k+1, where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

A. 3
B. 5
C. 17
D. 31
E. 257

option D ; check for all values k 0,1,2,3, so on.. only D does not matches.
Manager
Joined: 06 Nov 2016
Posts: 61
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Concentration: Strategy, International Business
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Re: Fermat primes are prime numbers that can be written in the form 2^k+1  [#permalink]

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16 Sep 2018, 21:52
1
Let x is a fermat prime, then $$x = 2^k + 1$$ --> $$x-1 = 2^k$$ --> $$x-1$$ is a power of 2
Subtract 1 from each answer choice, only D. 31-1=30 isn't a power of 2.

Bunuel wrote:
Fermat primes are prime numbers that can be written in the form $$2^k+1$$, where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

A. 3
B. 5
C. 17
D. 31
E. 257

_________________
Re: Fermat primes are prime numbers that can be written in the form 2^k+1 &nbs [#permalink] 16 Sep 2018, 21:52
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# Fermat primes are prime numbers that can be written in the form 2^k+1

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