# May I get a comment on this proof?

1. Oct 26, 2011

### flyingpig

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

Prove directly:

Prove that if $$2^{2x}$$ is odd integer, then $$4^{x}$$ is odd integer

3. The attempt at a solution

$$2^{2x} = 2k + 1$$ for some k is integer

$$2^{2x} = 4^{x} = 2k + 1$$

Thus completes the proof?

Am I allow to make the assumption (fact) $$2^{2x} = 4^{x}$$?

Thanks

2. Oct 26, 2011

### micromass

That is correct. It is indeed true that $a^{bc}=(a^b)^c$.

3. Oct 26, 2011

### flyingpig

nvm...I am just being an idiot

4. Oct 26, 2011

### ArcanaNoir

That's okay, sometimes I get concerned when things are trivial too.