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An algebra prove question 
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#1
Mar911, 06:54 PM

P: 8

1. The problem statement, all variables and given/known data
Prove that if one of the numbers 2^{n}1 and 2^{n}+1 is prime, n>2, then the other number is not 2. Relevant equations 3. The attempt at a solution 


#3
Mar911, 07:27 PM

P: 8

I dont even know how to start.



#4
Mar911, 08:35 PM

Mentor
P: 21,215

An algebra prove question
Part 1: Pick one of the numbers, and assume it is a prime larger than 2. Then show that the other number is not prime.
Part 2: Now pick the other number, and assume it is a prime larger than 2. Then show that the other number is not prime. 


#5
Mar1911, 11:32 PM

P: 44

I dont know.....it the result is correct but.....2^n1 is prime when n is an odd number.....not all odd number but n has to be of the odd form.......and 2^n+1 is prime.....when n is some even number.....
can somebody tell me if it is correct...... 


#6
Mar2011, 12:41 AM

P: 7

Have you thought about using mathematical induction?
Set up your base case: n = 3 You will show that [tex]2^31 = 8  1 = 7[/tex] is prime and [tex]2^3 + 1 = 9 [/tex] is not since [tex] 9 = 3 \cdot 3[/tex]. Assume that it's true for n. Then prove the case for n + 1. 


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