Question 107
For how many positive integers $n \leq 1000$ does the equation in real numbers
$$
x^{\lfloor x\rfloor}=n
$$
have a positive solution for $x$? (For a real number $x$, $\lfloor x\rfloor$ denotes the largest integer that is not greater than $x$.)
$$
x^{\lfloor x\rfloor}=n
$$
have a positive solution for $x$? (For a real number $x$, $\lfloor x\rfloor$ denotes the largest integer that is not greater than $x$.)