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An algebra prove question

by numberthree
Tags: algebra, prove
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numberthree
#1
Mar9-11, 06:54 PM
P: 8
1. The problem statement, all variables and given/known data

Prove that if one of the numbers 2n-1 and 2n+1 is prime, n>2, then the other number is not

2. Relevant equations



3. The attempt at a solution
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Char. Limit
#2
Mar9-11, 07:25 PM
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P: 1,951
What have you tried?
numberthree
#3
Mar9-11, 07:27 PM
P: 8
I dont even know how to start.

Mark44
#4
Mar9-11, 08:35 PM
Mentor
P: 21,280
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.
Suk-Sci
#5
Mar19-11, 11:32 PM
P: 44
I dont know.....it the result is correct but.....2^n-1 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......
semithinking
#6
Mar20-11, 12:41 AM
P: 7
Have you thought about using mathematical induction?

Set up your base case: n = 3
You will show that [tex]2^3-1 = 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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