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

1. Sep 17, 2006

mr_coffee

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. Sep 17, 2006

Gokul43201

Staff Emeritus
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.

3. Sep 17, 2006

vsage

I think it means if n is prime. The integer n seems to be superfluous information.

4. Sep 17, 2006

mr_coffee

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

5. Sep 17, 2006

d_leet

Just to clarify (-1)^(-1) IS equal to -1 not 1.

6. Sep 17, 2006

mr_coffee

hah whooops u are right, thanks