An algebra prove question

  1. 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. jcsd
  3. Char. Limit

    Char. Limit 1,986
    Gold Member

    What have you tried?
     
  4. I dont even know how to start.
     
  5. Mark44

    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.
     
  6. 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......
     
  7. 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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