Question 6
The product of all positive real numbers $x$ satisfying the equation $$
\sqrt[20]{x^{\log_{2026} x}} = 26x
$$ is an integer $P.$ Find the number of positive integer divisors of $P.$
\sqrt[20]{x^{\log_{2026} x}} = 26x
$$ is an integer $P.$ Find the number of positive integer divisors of $P.$