1. ## need some help

Thank you very much ThePerfectHacker. Oops, I accidentally deleted my post, was trying to edit my proof. Anyway, many thanks to you, ThePerfectHacker

2. Originally Posted by jackie
I'm not sure about my proof because it seems that I didn't show both ways because this is an iff statement.

One side of the proof is obvious. If $\displaystyle x^4 \equiv a$ is solvable then $\displaystyle (x^2)^2 \equiv a$ and so $\displaystyle x^2\equiv a$ is solvable.

3. Thank you ThePerfectHacker. So, what I did was irrelevant and not really related to the proof?

4. Originally Posted by jackie
Thank you ThePerfectHacker. So, what I did was irrelevant and not really related to the proof?
You proved if $\displaystyle x^2 \equiv a(\bmod p)$ has a solution then $\displaystyle x^4 \equiv a(\bmod p)$.