# An algebra prove question

by numberthree
Tags: algebra, prove
 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
 PF Patron P: 1,930 What have you tried?
 P: 8 I dont even know how to start.
Mentor
P: 19,694

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

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