2 problems

Eigenvalue-form conjecture. Every eigenvalue of $M_n$ has the form $\pm\frac{1}{s_{n,j}}$ for all odd $n\geq 5$. If this holds and $g_n(x)$ is irreducible for odd $n\geq 11$, then…

Let $n$ be odd with $n\geq 5$, let $M_n$ be the substitution matrix, and write its characteristic polynomial as … The coefficients of $q_n(x)$ in standard form are arranged accordi…