Homework Help: If x is odd, then 2^x + 3^x is also odd

1. Apr 12, 2010

epkid08

1. The problem statement, all variables and given/known data

Prove: If x is a positive odd integer, then $$2^x + 3^x$$ is also a positive odd integer.

3. The attempt at a solution

Assume x is odd; there exists an integer k such that x = 2k + 1. Then
$$2^x + 3^x = 2^{2k+1} + 3^{2k+1}$$

I don't know how to go about simplifying it from here.

2. Apr 12, 2010

Dick

Re: Proof

Is 2^x even or odd? What about 3^x? I'm a bit confused why they are specifying x odd. Isn't it true even if x is even?