Question 46
Find the maximum possible value of integer $k$ for which there exist distinct real numbers $x_1, x_2, \dots, x_k$ greater than $1$ such that
$$
\forall\ 1 \le i,j \le k : x_i^{[x_j]} = x_j^{[x_i]}
$$
(By $[x]$ we mean the greatest integer less than or equal to $x$.)
$$
\forall\ 1 \le i,j \le k : x_i^{[x_j]} = x_j^{[x_i]}
$$
(By $[x]$ we mean the greatest integer less than or equal to $x$.)