2 problems

Let $\beta(N)=\beta^+(N)\cdot\beta^-(N)$ be the base-phi expansion of the number $N$. Let $w$ be a word of length $m$, and let $R_{\cdot w}$ be the sequence of occurrences of numbe…

Melham's conjecture. For any positive integers $n,m$, there is a polynomial $P_{2m-1}(x)$ of degree $2m-1$ with integer coefficients such that