# An algebra prove question

1. Mar 9, 2011

### numberthree

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

2. Mar 9, 2011

### Char. Limit

What have you tried?

3. Mar 9, 2011

### numberthree

I dont even know how to start.

4. Mar 9, 2011

### Staff: Mentor

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. Mar 19, 2011

### Suk-Sci

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......

6. Mar 20, 2011

### semithinking

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.