Is this can be an integer $\sqrt[2z-1]{2mz+p_{n}}$?

Question

let the integers $z>2$, $m>1$ and a prime number $p_{n}\geq 3$.

is the following can be an integer for any value of $z,m$ and $p_{n}$ ?

$\sqrt[2z-1]{2mz+p_{n}}$

Answer 1

Well no, because lets take z = 3, m = 2 and p = 3. Then the expression would be

$(2*2*3 + 3)^(0.2) = 15^(0.2)$

Which is clearly not an integer.