1. The problem statement, all variables and given/known data Prove that if one of the numbers 2^{n}-1 and 2^{n}+1 is prime, n>2, then the other number is not 2. Relevant equations 3. The attempt at a solution
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.
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......
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.