Easy number theory proof?

geerant

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I intuitively understand the statement is true, but can't figure out how to go about an actual proof.

Any help would be greatly appreciated.

Prove that if x is any odd integer then (-1)x = -1

Thanks
 
I intuitively understand the statement is true, but can't figure out how to go about an actual proof.
Prove that if x is any odd integer then (-1)x = -1

If \(\displaystyle x\) is odd then \(\displaystyle \left( {\exists j \in \mathbb{Z}} \right)\left[ {x = 2j + 1} \right]\)

Note that \(\displaystyle (-1)^x=(-1)^{2j+1}=(-1)^{2j}(-1)^{1}\).
 
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