Find all positive integer $x$, $y$, $z$ such that $2x^{2x}-1=y^{z+1}$
I have tried to use LTE lemma but it didn't work.
I think my problem is $z+1$. I can not control it.
When I use LTE lemma, the purpose is proving one side is larger than another side, but I stuck in $z+1$.