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Proof for al integers n, if n is prime then (-1)^n = -1, can i use counter example?

  1. Sep 17, 2006 #1
    Hello everyone. I'm wondering if i'm allowed to use a counter example to disprove this. I'm not sure if i'm understanding the statement correctly though. THe directions are:
    Determine whether the statement is true or false. Justify your answer with a rpoof or a counterexample.

    Here is the question:
    FOr all integers n, if n is prime then (-1)^n = -1.

    If it says for ALL integers n, doesn't this mean negatives as well? If it said for All positive integers than wouldn't it be true? But if i let n = -1, i would get (-1)^(-1) = 1, not -1. But if they said, for all integers n, if n is prime..does this mean they are saying n > 1?
     
  2. jcsd
  3. Sep 17, 2006 #2

    Gokul43201

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    The assertion can be rewritten as: For all prime integers n, (-1)^n = -1

    Typically, the term 'primes' is restricted to the positive integers.

    Yes, you can use a counter example to disprove it.
     
  4. Sep 17, 2006 #3
    I think it means if n is prime. The integer n seems to be superfluous information.
     
  5. Sep 17, 2006 #4
    Would this be enough to prove it?
    For all integers n, if n is prime then (-1)^n = -1.

    False. By definition of a prime number, 2 is an integer and also prime. (-1)^(2) = 1 != -1.

    Thanks guys, i actually forgot 2 was a prime number until you said it could be proved with a counter example :blushing:
     
  6. Sep 17, 2006 #5
    Just to clarify (-1)^(-1) IS equal to -1 not 1.
     
  7. Sep 17, 2006 #6
    hah whooops u are right, thanks
     
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