An algebra prove question

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

Char. Limit

What have you tried?

numberthree

I dont 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 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

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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numberthree	An algebra prove question Tweet 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

Char. Limit Recognitions: Gold Member	What have you tried?

Mark44 Mentor	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	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	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.