Functional Identity Satisfied By The Spread Polynomials

Suppose that the field is not of characteristic 2. Denote $S_{n}(s)$ to be the $n$ th spread polynomial in some number $s$ . What are all possible values of $x$ such that $x$ is of type $Nat$ and that the m-set $[S_{57}(s) \enspace S_{2018}(s) \enspace S_{x}(s)]$ is a spread triple for any $s$ .

The definitions of the terms can be found here .