Can Mathematical Induction Prove the Primality of 2n-1 and 2n+1?

[numberthree]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

What have you tried?

 

[numberthree]

I don't even know how to start.

 

[Mark44]

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]

I don't 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]

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.